Statistical mechanics and dynamics of solvable models with long-range interactions

Abstract

The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^{\alpha }$, with $\alpha \le d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics, two-dimensional elasticity, charged and dipolar systems. Although such systems can be made extensive, they are intrinsically non additive. Moreover, the space of accessible macroscopic thermodynamic parameters might be non convex. The violation of these two basic properties is at the origin of ensemble inequivalence, which implies that specific heat can be negative in the microcanonical ensemble and temperature jumps can appear at microcanonical first order phase transitions. The lack of convexity implies that ergodicity may be generically broken. We present here a comprehensive review of the recent advances on the statistical mechanics and out-of-equilibrium dynamics of systems with long-range interactions. The core of the review consists in the detailed presentation of the concept of ensemble inequivalence, as exemplified by the exact solution, in the microcanonical and canonical ensembles, of mean-field type models. Relaxation towards thermodynamic equilibrium can be extremely slow and quasi-stationary states may be present. The understanding of such unusual relaxation process is obtained by the introduction of an appropriate kinetic theory based on the Vlasov equation.

118 pages, review paper, added references, slight change of content

References in corpus (95)

• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• SparsePak: A Formatted Fiber Field Unit for The WIYN Telescope Bench Spectrograph. I. Design, Construction, and Calibration
• A Dynamical Approach to Temperature
• Non-Gaussian equilibrium in a long-range Hamiltonian system
• Inequivalence of ensembles in a system with long range interactions
• Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
• Geometric approach to Hamiltonian dynamics and statistical mechanics
• Breaking of ergodicity and long relaxation times in systems with long-range interactions
• Bose Condensates with 1/r Interatomic Attraction: Electromagnetically Induced ``Gravity''
• Superdiffusion and Out-of-equilibrium Chaotic Dynamics with Many Degrees of Freedoms
• Long-range interacting rotators: connection with the mean--field approximation
• Classification of phase transitions and ensemble inequivalence, in systems with long range interactions
• Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models
• Phase transitions and configuration space topology
• A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model
• Out-of-equilibrium tricritical point in a system with long-range interactions
• Phase Transitions in "Small" systems
• Long-term Evolution of Stellar Self-Gravitating System away from the Thermal Equilibrium: connection with non-extensive statistics
• A Theorem on the origin of Phase Transitions
• Collisionless relaxation in non-neutral plasmas
• Kinetic theory of point vortices: diffusion coefficient and systematic drift
• On first-order phase transition in microcanonical and canonical non-extensive systems
• Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system
• Collisionless relaxation in gravitational systems: From violent relaxation to gravothermal collapse
• Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation
• Stability and ensemble inequivalence in a globally coupled system
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
• Kinetic theory of point vortices in two dimensions: analytical results and numerical simulations
• Quasi-equilibria in one-dimensional self-gravitating many body systems
• Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows
• Equilibrium and dynamical properties of two dimensional self-gravitating systems
• Topological Signature of First Order Phase Transitions
• Canonical Solution of Classical Magnetic Models with Long-Range Couplings
• Hamiltonian and Brownian systems with long-range interactions
• The Vlasov equation and the Hamiltonian Mean-Field model
• On the diffusive anomalies in a long-range Hamiltonian system
• Thermodynamics of the self-gravitating ring model
• Phase transition in the collisionless regime for wave-particle interaction
• Long time behavior of quasi-stationary states of the Hamiltonian Mean-Field model
• Violation of the Zeroth Law of Thermodynamics in Systems with Negative Specific Heat
• Phase space gaps and ergodicity breaking in systems with long range interactions
• Phase transitions and topology changes in configuration space
• Partial equivalence of statistical ensembles and kinetic energy
• Origin of scaling structure and non-gaussian velocity distribution in self-gravitating ring model
• Hamiltonian dynamics reveals the existence of quasi-stationary states for long-range systems in contact with a reservoir
• The stochastic process of equilibrium fluctuations, of a system with long range interactions
• Thermodynamic Limit for Dipolar Media
• Statistical mechanics of the shallow water system
• Dynamics and thermodynamics of rotators interacting with both long and short range couplings
• Incomplete equilibrium in long-range interacting systems
• Relaxation of the distribution function tails for systems described by Fokker-Planck equations
• The mean-field phi4-model: entropy, analyticity, and configuration space topology
• Ensemble inequivalence in systems with long-range interactions
• Violation of ensemble equivalence in the antiferromagnetic mean-field XY model
• Topology and Phase Transitions II. Theorem on a necessary relation
• Topology and Phase Transitions I. Preliminary Results
• Negative magnetic susceptibility and nonequivalent ensembles for the mean-field ${\varphi }^4$ spin model
• Controlled switching of intrinsic localized modes in a 1-D antiferromagnet
• Modeling long-range memory with stationary Markovian processes
• Hamiltonian and Brownian systems with long-range interactions: III. The BBGKY hierarchy for spatially inhomogeneous systems
• Metastable states, anomalous distributions and correlations in the HMF model
• Application of large deviation theory to the mean-field phi^4-model
• Long-Range Effects in Layered Spin Structures
• Topological origin of the phase transition in a mean-field model
• Topology and phase transitions: from an exactly solvable model to a relation between topology and thermodynamics
• Microcanonical quasi-stationarity of long-range interacting systems in contact with a heat bath
• The Non--Ergodicity Threshold: Time Scale for Magnetic Reversal
• Hamiltonian and Brownian systems with long-range interactions: IV. General kinetic equations from the quasilinear theory
• Microcanonical solution of the mean-field ${\varphi }^4$ model: comparison with time averages at finite size
• Phase transitions induced by saddle points of vanishing curvature
• Out-of-equilibrium states as statistical equilibria of an effective dynamics
• On the inequivalence of statistical ensembles
• On the mean-field spherical model
• Phase Transitions in Finite Systems using Information Theory
• Relaxation of a test particle in systems with long-range interactions: diffusion coefficient and dynamical friction
• The topological hypothesis on phase transitions: the simplest case
• Emergence of power-law correlation in 1-dimensional self-gravitating system
• Phase Transitions from Saddles of the Potential Energy Landscape
• Antonov problem and quasi-equilibrium states in N-body system
• First and second order clustering transitions for a system with infinite-range attractive interaction
• Nonanalyticities of entropy functions of finite and infinite systems
• Glassy dynamics in the HMF model
• Ensemble inequivalence in random graphs
• Out of equilibrium phase transitions in mean field Hamiltonian dynamics
• Thermodynamic fluctuation relation for temperature and energy
• Statistical mechanics of two-dimensional vortices and stellar systems
• Topology, phase transitions and the spherical model
• Counting discrete emission steps from intrinsic localized modes in a quasi-1D antiferromagnetic lattice
• Topological approach to phase transitions and inequivalence of statistical ensembles
• Microcanonical solution of lattice models with long range interactions
• Nonextensive scaling in a long-range Hamiltonian system
• Vlasov stability of the Hamiltonian Mean Field model
• On the nonextensivity of the long range X-Y model
• Phase transitions and topology in 2+k XY mean-field models
• On the dynamical anomalies in the Hamiltonian Mean Field model

Cited by in corpus (533)

• The large deviation approach to statistical mechanics
• Quantum many-body models with cold atoms coupled to photonic crystals
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
• Spread of correlations in long-range interacting quantum systems
• Long-range interacting quantum systems
• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
• Understanding quantum measurement from the solution of dynamical models
• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Thermodynamics and dynamics of systems with long-range interactions
• Review of Some Promising Fractional Physical Models
• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects
• Correlation-induced localization
• Collective dynamics in a binary mixture of hydrodynamically coupled micro-rotors
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• Diverging equilibration times in long-range quantum spin models
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• The role of correlations in the collective behaviour of microswimmer suspensions
• Breaking of ensemble equivalence in networks
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Dramatic acceleration of wave condensation mediated by disorder in multimode fibers
• Self-assembly of colloidal molecules due to self-generated flow
• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Kinetic theory of long-range interacting systems with angle-action variables and collective effects
• Persistent Homology analysis of Phase Transitions
• Core-halo distribution in the Hamiltonian Mean-Field Model
• Kinetic theory of spatially inhomogeneous stellar systems without collective effects
• Chimeras in SQUID Metamaterials
• Thermodynamic limits of dynamic cooling
• Kinetic theory of jet dynamics in the stochastic barotropic and 2D Navier-Stokes equations
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• Models of dark matter halos based on statistical mechanics: II. The fermionic King model
• Most energetic passive states
• Muscle as a meta-material operating near a critical point
• Prethermalization of atoms due to photon-mediated long-range interactions
• Slow relaxation in long-range interacting systems with stochastic dynamics
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Thermal and non-thermal signatures of the Unruh effect in Casimir-Polder forces
• Influence of long-range interactions on the critical behavior of the Ising model
• Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems
• Highly nonlocal optical nonlinearities in atoms trapped near a waveguide
• Coulomb and Riesz gases: The known and the unknown
• Large deviation approach to nonequilibrium systems
• Liquid-Gas phase transition in nuclei
• Models of dark matter halos based on statistical mechanics: I. The classical King model
• Physics of muscle contraction
• Metastability and discrete spectrum of long-range systems
• Statistical Mechanics of Systems with Negative Temperature
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Nonequivalence of ensembles for long-range quantum spin systems in optical lattices
• Phase space mass bound for fermionic dark matter from dwarf spheroidal galaxies
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Quasi-stationary states in the self-gravitating sheet model
• Non-Fourier heat transport in nanosystems
• Quantum kinetics of ultracold fermions coupled to an optical resonator
• Solvable phase diagrams and ensemble inequivalence for two-dimensional and geophysical turbulent flows
• Criticality of Spin Systems with Weak Long-Range Interactions
• Dynamics of colloidal particles with capillary interactions
• Kinetic equations for systems with long-range interactions: a unified description
• Quasi-stationary states and the range of pair interactions
• The world of long-range interactions: A bird's eye view
• Relaxation to thermal equilibrium in the self-gravitating sheet model
• Nonequilibrium first-order transition in coupled oscillator systems with inertia and noise
• Bifurcations and singularities for coupled oscillators with inertia and frustration
• Thermodynamics of nonadditive systems
• Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs
• Universal threshold for the dynamical behavior of lattice systems with long-range interactions
• Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Approach to equilibrium of diffusion in a logarithmic potential
• Quenches across the self-organization transition in multimode cavities
• Critical Casimir Effect: Exact Results
• Lattice Model of Fractional Gradient and Integral Elasticity: Long-Range Interaction of Grunwald-Letnikov-Riesz Type
• Quantum quench in long-range field theories
• Interplay of Soundcone and Supersonic Propagation in Lattice Models with Power Law Interactions
• Absence of thermalization for systems with long-range interactions coupled to a thermal bath
• Aging in the long-range Ising model
• Does the brain behave like a (complex) network? I. Dynamics
• Brownian particles with long and short range interactions
• Role of the range of the interactions in thermal conduction
• Ensemble equivalence for general many-body systems
• Shock waves in capillary collapse of colloids: a model system for two--dimensional screened Newtonian gravity
• Nonequilibrium stationary states of 3D self-gravitating systems
• Spreading of Perturbations in Long-Range Interacting Classical Lattice Models
• Phase transitions in systems with non-additive long-range interactions
• Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems
• Analytical study of kinklike structures with polynomial tails
• Extracting maximum power from active colloidal heat engines
• Long-range gravitational-like interaction in a neutral atomic cold gas
• Finite-temperature critical behavior of long-range quantum Ising models
• Ergodicity Breaking and Parametric Resonances in Systems with Long-Range Interactions
• Validity and Failure of the Boltzmann Weight
• Ecological feedback in quorum-sensing microbial populations can induce heterogeneous production of autoinducers
• Thermal transport in long-range interacting Fermi-Pasta-Ulam chains
• Dissipation-assisted prethermalization in long-range interacting atomic ensembles
• Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges
• Lattice with Long-Range Interaction of Power-Law Type for Fractional Non-Local Elasticity
• Interaction between kinks and antikinks with double long-range tails
• Statistical theory of quasi stationary states beyond the single water-bag case study
• Dynamical phase transitions to optomechanical superradiance
• Gravity and Nonequilibrium Thermodynamics of Classical Matter
• Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems
• The Brownian Mean Field model
• Complex networks embedded in space: Dimension and scaling relations between mass, topological distance and Euclidean distance
• Dipolar needles in the microcanonical ensemble: evidence of spontaneous magnetization and ergodicity breaking
• Instability of the mean-field states and generalization of phase separation in long-range interacting systems
• Prethermalization in the transverse-field Ising chain with long-range interactions
• Relaxation in self-gravitating systems
• Dynamical scaling of correlations generated by short- and long-range dissipation
• Eigenstate Thermalization in Long-Range Interacting Systems
• Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model
• Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas
• Inhomogeneous Tsallis distributions in the HMF model
• Energy current correlation in solvable long-range interacting systems
• One dimensional phase-ordering in the Ising model with space decaying interactions
• Wave condensation with weak disorder versus beam self-cleaning in multimode fibers
• Criticality of relaxation in dislocation systems
• Self-consistent inhomogeneous steady states in Hamiltonian mean field dynamics
• Stationary states and fractional dynamics in systems with long range interactions
• Kinetic theory of Onsager's vortices in two-dimensional hydrodynamics
• Chaos in the Hamiltonian mean field model
• Thermodynamics and dynamics of atomic self-organization in an optical cavity
• Generalized Higgs mechanism in long-range interacting quantum systems
• Scaling with system size of the Lyapunov exponents for the Hamiltonian Mean Field model
• Quasistationarity in a model of classical spins with long-range interactions
• Energy transport in the presence of long-range interactions
• Entropy principle and complementary second law of thermodynamics for self-gravitating systems
• Out-of-equilibrium phase transitions in the HMF model: a closer look
• Long-range multi-scalar models at three loops
• Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model
• Modulational instabilities in lattices with power-law hoppings and interactions
• Nonequilibrium phase transitions in systems with long-range interactions
• Fractional Liouville Equation on Lattice Phase-Space
• Linear response theory for long-range interacting systems in quasistationary states
• Nano-friction in cavity quantum electrodynamics
• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• Critical behaviour of the XY -rotors model on regular and small world networks
• Ensemble nonequivalence in random graphs with modular structure
• Restricted Equilibrium and the Energy Cascade in Rotating and Stratified Flows
• Long-range correlations and ensemble inequivalence in a generalized ABC model
• Many-body enhancement in a spin-chain quantum heat engine
• Vlasov equation for long-range interactions on a lattice
• Self-gravitating Brownian particles in two dimensions: the case of N=2 particles
• Kinetic theory of nonequilibrium stochastic long-range systems: Phase transition and bistability
• Phase transitions in self-gravitating systems and bacterial populations with a screened attractive potential
• Nonequivalence of ensembles in the Curie-Weiss anisotropic quantum Heisenberg model
• Fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of long-range interacting systems
• Novel Dynamics and Thermodynamics in systems with long range interactions
• Controlling the Range of Interactions in the Classical Inertial Ferromagnetic Heisenberg Model: Analysis of Metastable States
• Long-range interacting systems in the unconstrained ensemble
• Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method
• Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature
• Statistical mechanics of systems with long-range interactions and negative absolute temperature
• Traveling Solitons in Long-Range Oscillator Chains
• Diffusion in a logarithmic potential: scaling and selection in the approach to equilibrium
• Dynamical quantum phase transition in a bosonic system with long-range interactions
• Dynamical robustness of network of oscillators
• Dynamics and physical interpretation of quasi-stationary states in systems with long-range interactions
• Mean-field phase diagram of ultracold atomic gases in cavity quantum electrodynamics
• Instabilities and relaxation to equilibrium in long-range oscillator chains
• Large Lattice Fractional Fokker-Planck Equation
• Phase-space interference in extensive and non-extensive quantum heat engines
• Dynamical fluctuations in the Riesz gas
• Caloric curves of self-gravitating fermions in general relativity
• The ambiguity of nestedness under soft and hard constraints
• Collective dynamics of colloids at fluid interfaces
• The catalytic role of beta effect in barotropization processes
• Invariant measures of the 2D Euler and Vlasov equations
• Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions
• Kinetic theory of collisionless relaxation for systems with long-range interactions
• Quantum phase transition in the spin-anisotropic quantum spherical model
• Long-range interaction induced collective dynamical behaviors
• Gravitational phase transitions and instabilities of self-gravitating fermions in general relativity
• Ensemble inequivalence in the Blume-Emery-Griffiths model near a fourth order critical point
• Beam-Plasma Instability and Fast Particles: the Lynden-Bell Approach
• Noise-induced dynamical phase transitions in long-range systems
• Thermodynamics is more powerful than the role to it reserved by Boltzmann-Gibbs statistical mechanics
• Freezing transition in the barrier crossing rate of a diffusing particle
• Collisional relaxation in the inhomogeneous Hamiltonian-Mean-Field model: diffusion coefficients
• Geometrically confined thermal field theory: Finite size corrections and phase transitions
• Random transitions described by the stochastic Smoluchowski-Poisson system and by the stochastic Keller-Segel model
• Additional Invariants and Statistical Equilibria for the 2D Euler Equations on a spherical domain
• Multicanonical entropy like-solution of statistical temperature weighted histogram analysis method (ST-WHAM)
• Universality in the time correlations of the long-range 1d Ising model
• Gravothermal Catastrophe: the dynamical stability of a fluid model
• Energy landscape and phase transitions in the self-gravitating ring model
• Remarks about the thermodynamics of astrophysical systems in mutual interaction and related notions
• Planelike interfaces in long-range Ising models and connections with nonlocal minimal surfaces
• Coexistence of coarsening and mean field relaxation in the long-range Ising chain
• Strong ensemble nonequivalence in systems with local constraints
• Collective waves in dense and confined microfluidic droplet arrays
• Topological Approach to Microcanonical Thermodynamics and Phase Transition of Interacting Classical Spins
• Surprises from quenches in long-range interacting systems: Temperature inversion and cooling
• Kinetic theory for non-equilibrium stationary states in long-range interacting systems
• Long-lived transient structure in collisionless self-gravitating systems
• Fluctuations in interacting particle systems with memory
• Models with short and long-range interactions: phase diagram and reentrant phase
• Large deviations in models of growing clusters with symmetry-breaking transitions
• Velocity filtration and temperature inversion in a system with long-range interactions
• Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations
• Mean-field theory of atomic self-organization in optical cavities
• Kinetic theory of two-dimensional point vortices with collective effects
• Work extraction from microcanonical bath
• Power-law Spatial Dispersion from Fractional Liouville Equation
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Non-equilibrium Statistical Mechanics of Two-dimensional Vortices
• Stroboscopic aliasing in long-range interacting quantum systems
• Swimming suppresses correlations in dilute suspensions of pusher microorganisms
• Quasi-deterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets
• Ensemble in-equivalence in supernova matter within a simple model
• Microscopic Aspects of Magnetic Lattice Demagnetizing Factors
• Spectral and formal stability criteria of spatially inhomogeneous stationary solutions to the Vlasov equation for the Hamiltonian mean-field model
• Existence of Quasi-stationary states at the Long Range threshold
• Large scale Micro-Photometry for high resolution pH-characterization during electro-osmotic pumping and modular micro-swimming
• Action diffusion and lifetimes of quasistationary states in the Hamiltonian Mean Field model
• Caloric curves of classical self-gravitating systems in general relativity
• Violent relaxation in quantum fluids with long-range interactions
• A statistical-mechanical explanation of dark matter halo properties
• Tsallis entropy induced metrics and CAT(k) spaces
• Formation and relaxation of quasi-stationary states in particle systems with power law interactions
• Emergence of a non trivial fluctuating phase in the XY model on regular networks
• Caloric curve of star clusters
• Physical interpretation of the canonical ensemble for long-range interacting systems in the absence of ensemble equivalence
• Quantum critical behavior of entanglement in lattice bosons with cavity-mediated long-range interactions
• Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere
• The F-theorem in the melonic limit
• Gravothermal Catastrophe with a Cosmological Constant
• Observation of type-III corner states induced by long-range interactions
• Long-range interacting systems are locally non-interacting
• Long-range interactions, doubling measures and Tsallis entropy
• Superradiant optomechanical phases of cold atomic gases in optical resonators
• Harmonically confined long-ranged interacting gas in the presence of a hard wall
• Ordering Kinetics of the two-dimensional voter model with long-range interactions
• Logarithmic corrections to the entropy function of black holes in the open ensemble
• Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials
• Effects of energy extensivity on the quantum phases of long-range interacting systems
• Condensation vs Ordering: From the Spherical Models to BEC in the Canonical and Grand Canonical Ensemble
• Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics
• Solving the Vlasov equation for one-dimensional models with long range interactions on a GPU
• Ewald Sums for One Dimension
• Caloric curves fitted by polytropic distributions in the HMF model
• Partitioning a macroscopic system into independent subsystems
• Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings
• Relaxation dynamics of stochastic long-range interacting systems
• First-order phase transitions from poles in asymptotic representations of partition functions
• Experimental perspectives for systems based on long-range interactions
• Quasistationarity in a long-range interacting model of particles moving on a sphere
• The Origin of Mean-Field Behavior in an Elastic Ising Model
• Ensemble Inequivalence in the Ferromagnetic p-spin Model in Random Fields
• On a microcanonical relation between continuous and discrete spin models
• Concavity, Response Functions and Replica Energy
• $N$-body chaos and the continuum limit in numerical simulations of self-gravitating systems, revisited
• Phase diagram of the ABC model with nonconserving processes
• Symmetry Breaking in d-Dimensional Self-gravitating Systems
• Scaling quasi-stationary states in long range systems with dissipation
• Macroscopic Length Correlations in Non-Equilibrium Systems and Their Possible Realizatons
• Thermodynamics of the HMF model with a magnetic field
• Collisional relaxation of two-dimensional self-gravitating systems
• Gravitational phase transitions with an exclusion constraint in position space
• Solvable model of a self-gravitating system
• Heat transport in long-ranged anharmonic oscillator models
• Spontaneous synchronization and nonequilibrium statistical mechanics of coupled phase oscillators
• Regular and bistable steady-state superradiant phases of an atomic beam traversing an optical cavity
• Non equivalence of dynamical ensembles and emergent non ergodicity
• Monitored long-range interacting systems: spin-wave theory for quantum trajectories
• Phases of cold atoms interacting via photon-mediated long-range forces
• Ensemble Inequivalence and the Spin-Glass Transition
• Statistical mechanics of two-dimensional point vortices: relaxation equations and strong mixing limit
• Coarsening and metastability of the long-range voter model in three dimensions
• Statistical mechanics of collisionless relaxation in a noninteracting system
• Linear theory and violent relaxation in long-range systems: a test case
• Memristive Networks: from Graph Theory to Statistical Physics
• Microcanonical characterization of first-order phase transitions in a generalized model for aggregation
• Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit
• Dynamical robustness of complex networks subject to long-range connectivity
• Synchronization and collective motion of globally coupled Brownian particles
• Phase transitions in simplified models with long-range interactions
• First-passage functionals of Brownian motion in logarithmic potentials and heterogeneous diffusion
• Inverse Ising problem for one-dimensional chains with arbitrary finite-range couplings
• Violent relaxation in the Hamiltonian Mean Field model: I. Cold collapse and effective dissipation
• Thermal contribution of unstable states
• Origin of Negative Temperatures in Systems Interacting with External Fields
• Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems
• Study of the long-range transverse field Ising model with fermionic Gaussian states
• Ensemble inequivalence : Landau theory and the ABC model
• Gravitational instabilities of isothermal spheres in the presence of a cosmological constant
• Self-consistent harmonic approximation with non-local couplings
• Statistical Mechanics of Gravitational Systems with Regular Orbits: Rigid Body Model of Vector Resonant Relaxation
• Ensemble inequivalence in long-range quantum systems
• Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions
• Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying Density-Density Interactions
• Equilibration in long-range quantum spin systems from a BBGKY perspective
• Overdamped dynamics of long-range systems on a one-dimensional lattice: Dominance of the mean-field mode and phase transition
• Ferromagnetic phases due to competing short- and long-range interactions in the spin-S Blume-Capel model
• Groups, non-additive entropy and phase transitions
• Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics
• Methods for calculating nonconcave entropies
• Coupled spin models for magnetic variation of planets and stars
• The grand canonical ABC model: a reflection asymmetric mean field Potts model
• $N$-Scaling of Timescales in Long-Range $N$-Body Quantum Systems
• Phase transitions in Thirring's model
• Balancing long-range interactions and quantum pressure: solitons in the HMF model
• Non-thermodynamic nature of the orbital angular momentum in neutral fermionic superfluids
• A sluggish random walk with subdiffusive spread
• Classical Heisenberg spins with long-range interactions: Relaxation to equilibrium for finite systems
• Low-frequency discrete breathers in long-range systems without on-site potential
• Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation
• Attractor non-equilibrium stationary states in perturbed long-range interacting systems
• Strange Scaling and Temporal Evolution of Finite-Size Fluctuation in Thermal Equilibrium
• Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example
• Finite-size versus finite-temperature effects in the critical long-range $O(N)$ model
• Fluctuation relations for equilibrium states with broken discrete or continuous symmetries
• Kinetics of the one-dimensional voter model with long-range interactions
• Ergodicity in a two-dimensional self gravitating many body system
• Violent relaxation in the Hamiltonian mean field model: II. Non-equilibrium phase diagrams
• Current fluctuations in the Dyson Gas
• On the foundations of statistical mechanics
• Stability of inhomogeneous states in mean-field models with a local potential
• Light induced "Mock Gravity" at the nanoscale
• Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales
• Density profiles of a self-gravitating lattice gas in one, two, and three dimensions
• Simulating long-range hopping with periodically-driven superconducting qubits
• (Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
• Incoherent localized structures and hidden coherent solitons from the gravitational instability of the Schrödinger-Poisson equation
• A mean-field model of memristive circuit interaction
• Lyapunov Exponent and Criticality in the Hamiltonian Mean Field Model
• Topology of Collisionless Relaxation
• On the Apparent Power Law in CDM Halo Pseudo Phase Space Density Profiles
• Sampling microcanonical measures of the 2D Euler equations through Creutz's algorithm: a phase transition from disorder to order when energy is increased
• Macrostate equivalence of two general ensembles and specific relative entropies
• Trapping scaling for bifurcations in Vlasov systems
• Non-equilibrium steady states of long-range coupled harmonic chains
• Static kinks in chains of interacting atoms
• Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures
• Stability and decay of subradiant patterns in a quantum gas with photon-mediated interactions
• Collective $1/f$ fluctuation by pseudo-Casimir-invariants
• Transformer Wave Function for Quantum Long-Range models
• Entropy production in systems with long range interactions
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
• Crafting networks to achieve, or not achieve, chaotic states
• Lieb-Schultz-Mattis theorem in higher dimensions from approximate magnetic translation symmetry
• Monte Carlo simulations in the unconstrained ensemble
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions
• Aging properties of the voter model with long-range interactions
• Conformal order and Poincar$\acute{\mathrm{e}}$-Klein mapping underlying electrostatics-driven inhomogeneity in tethered membranes
• Universality in long-range interacting systems: the effective dimension approach
• Comparative Microscopic Study of Entropies and their Production
• Ensemble Inequivalence in Systems with Wave-Particle Interaction
• Ensemble nonequivalence and Bose-Einstein condensation in weighted networks
• Formation of disks with long-lived spiral arms from violent gravitational dynamics
• Exciting out-of-equilibrium states in macromolecules through light pumping
• Density of states of continuous and discrete spin models: a case study
• Kinked Entropy and Discontinuous Microcanonical Spontaneous Symmetry Breaking
• Mean-field theory is exact for the random-field model with long-range interactions
• The study of the dynamics of the order parameter of coupled oscillators in the Ott-Antonsen scheme for generic frequency distributions
• Phase diagram of neutron-rich nuclear matter and its impact on astrophysics
• General linear response formula for non integrable systems obeying the Vlasov equation
• Geometry of the energy landscape of the self-gravitating ring
• Generalized maximum entropy approach to quasi-stationary states in long range systems
• Functionality of disorder in muscle mechanics
• Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions
• Coarse-grained collisionless dynamics with long-range interactions
• Phase transitions in the unconstrained ensemble
• Entropy production and Vlasov equation for self-gravitating systems
• Nonequilibrium thermodynamic process with hysteresis and metastable states -- A contact Hamiltonian with unstable and stable segments of a Legendre submanifold
• Conditions for predicting quasistationary states by rearrangement formula
• Influence of long-range interaction on degeneracy of eigenvalues of connection matrix of d-dimensional Ising system
• Ensemble Inequivalence and Maxwell Construction in the Self-Gravitating Ring Model
• Nonadditivity in Quasiequilibrium States of Spin Systems with Lattice Distortion
• Long-time equilibration can determine transient thermality
• Computational Statistical Mechanics of a confined, three-dimensional Coulomb gas
• Thermodynamic instabilities in holographic neutron stars at finite temperature
• Quantum memory at an eigenstate phase transition in a weakly chaotic model
• Novel lumplike structures
• Energy barriers between metastable states in first order quantum phase transitions
• Hamiltonian mean field model : effect of temporal perturbation in coupling matrix
• Asymptotic equivalence of probability measures and stochastic processes
• Importance-sampling computation of statistical properties of coupled oscillators
• Lifetime of locally stable states near a phase transition in the Thirring model
• Enhancing strength and range of atom-atom interaction in a coupled-cavity array via parametric drives
• Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system
• Re-equilibration after quenches in athermal martensites:Conversion-delays for vapour to liquid domain-wall phases
• Non-diagonalizable and non-divergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions
• Finite $N$ corrections to Vlasov dynamics and the range of pair interactions
• Transformation between statistical ensembles in the modelling of nuclear fragmentation
• Many-body spin glasses in the microcanonical ensemble
• Temperature gradients in equilibrium: small microcanonical systems in an external field
• Double Lynden-Bell Structure of Low-Energy Quasi-Stationary Distributions in the Hamiltonian Mean-Field Model
• Gravothermal instability with a cosmological constant in the canonical ensemble
• Landau kinetic equation for dry aligning active models
• Prethermalization with negative specific heat
• From conformal invariance to quasistationary states
• Ensemble equivalence in spin systems with short-range interactions
• Equilibration in the Nosé-Hoover isokinetic ensemble: Effect of inter-particle interactions
• Second-order solutions of the equilibrium statistical mechanics for self-gravitating systems
• Brownian regime of finite-N corrections to particle motion in the XY hamiltonian mean field model
• Microcanonical Analysis of Spin Glasses Using Gauge Symmetry
• Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample
• On the probabilistic approach to the N-body problem
• Tsallis entropy composition and the Heisenberg group
• Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant
• Phase Crossover induced by Dynamical Many Body Localization in Periodically Driven Long-Range Spin Systems
• Thermodynamics of gravitational clustering phenomena: $N$-body self-gravitating gas on the sphere ${\mathbb{S}}^3\subset {\mathbb{R}}^4$
• Functional integral approach to the kinetic theory of inhomogeneous systems
• Computation of microcanonical entropy at fixed magnetization without direct counting
• Phase transitions of quasistationary states in the Hamiltonian Mean Field model
• Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces
• The vmf90 program for the numerical resolution of the Vlasov equation for mean-field systems
• Optimizing quantum sensing networks via genetic algorithms and deep learning
• Finite-size Nagle-Kardar model: Casimir force
• First- and second-order quantum phase transitions in the long-range unfrustrated antiferromagnetic Ising chain
• On the new universality class in structurally disordered $n$-vector model with long-range interactions
• Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• A pure non-neutral plasma under an external harmonic field: equilibrium thermodynamics and chaos
• Theory of Critical Phenomena with Memory
• A Simple Model for Long-Range Interacting Pendula
• Linear and non-linear instabilities of Kirchhoff's Elliptical Vortices
• On the effectiveness of mixing in violent relaxation
• Using Kernel-Based Statistical Distance to Study the Dynamics of Charged Particle Beams in Particle-Based Simulation Codes
• Holographic pressure and volume for black holes
• Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement
• Relaxation Processes in Long-Range Lattices
• Quantum frustrated Wigner chains
• Critical exponents in mean-field classical spin systems
• The quasilinear theory in the approach of long-range systems to quasi-stationary states
• An Introduction to Large Deviations and Equilibrium Statistical Mechanics for Turbulent Flows
• Ensemble inequivalence and absence of quasi-stationary states in long-range random networks
• How Geometrical Frustrated Systems Challenge our Notion of Thermodynamics
• Differences in the scaling laws of canonical and microcanonical coarsening dynamics for long-range interacting systems
• Tricritical point in the quantum Hamiltonian mean-field model
• Fractal ground state of ion chains in periodic potentials
• Solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction
• Laminar-Turbulent Transition: The change of the flow state temperature with the Reynolds number
• Caloric curve for nuclear liquid-gas phase transition in relativistic mean-field hadronic model
• Energy diffusion in the long-range interacting spin systems
• Some aspects of the phase diagram of nuclear matter relevant to compact stars
• Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions
• Dynamics to the universal structure of one-dimensional self-gravitating systems in the quasi-equilibrium state
• Multispecies reaction diffusion models and the Turing instability revisited
• Emergence of a collective crystal in a classical system with long-range interactions
• Thermal transport in long-range interacting harmonic chains perturbed by long-range conservative noise
• Zeroth Law in Quantum Thermodynamics at Strong Coupling: `in Equilibrium', not `Equal Temperature'
• Master Equation for a Quantum Gas of Polarizable Particles in Cavities
• Scalar correlators and normal modes in holographic neutron stars
• Dynamic critical exponent in quantum long-range models
• Fractional Dynamics and Modulational Instability in Long-Range Heisenberg Chains
• Quantum fluctuations inhibit symmetry breaking in the HMF model
• Poles, Shocks and Tygers: The Time-reversible Burgers equation
• Winding number excitation detects phase transition in one-dimensional XY model with variable interaction range
• Dynamics of random dipoles : chaos {\it vs} ferromagnetism
• Effective negative specific heat by destabilization of metastable states in dipolar systems
• Dynamical Spreading and Memory Retention Under Power Law Potential
• Fluids with power-law repulsion: Hyperuniformity and energy fluctuations
• Ensemble Inequivalence in Long-Range Quantum Spin Systems
• Fractional diffusion without disorder in two dimensions
• Violent relaxation in one-dimensional self-gravitating system: deviation from the Vlasov limit due to finite-$N$ effect
• Domain Growth in Long-range Ising Models with Disorder
• Core-Halo Quasi-Stationary States in the Hamiltonian Mean-Field Model
• A stochastic model of long-range interacting particles
• Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
• Experimental evidence for long-distance electrodynamic intermolecular forces
• Clausius' theorem and the Second law in the process of isoenergetic thermalization
• Perturbation theory for very long-range potentials
• A core-halo pattern of entropy creation in gravitational collapse
• Switch between critical percolation modes in city traffic dynamics
• Vlasov dynamics of 1D models with long-range interactions
• Nonequilibrium steady state in a large magneto-optical trap
• Classical Goldstone modes in Long-Range Interacting Systems
• Ensemble Equivalence for Counterion Condensation on a Two Dimensional Charged Disc
• Pulse solutions of the fractional effective models of the Fermi-Pasta-Ulam lattice with long-range interactions
• Geometrically Frustrated Systems which are as Singles Hotter Than in Company
• Temperature fluctuations in finite systems: Application to the one-dimensional Ising chain
• Modified Thirring model beyond the excluded-volume approximation
• Long time behaviour of interacting particles through a vibrating medium: comparison between the N-particle systems and the natural kinetic equation dynamics
• Meta-conformal algebras in $d$ spatial dimensions
• Mass Segregation Phenomena using the Hamiltonian Mean Field Model
• Dynamics of coupled oscillator systems in presence of a local potential
• Renewal stochastic processes with correlated events. Phase transitions along time evolution
• Relaxation to equilibrium in models of classical spins with long-range interactions
• Ensemble equivalence for mean field models and plurisubharmonicity
• Thermodynamics of fluctuations in small systems interacting with the environment
• Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions
• Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks
• Negative heat capacity for hot nuclei using formulation from the microcanonical ensemble INDRA Collaboration
• A condensed-matter analogue of the false vacuum
• Extensive Nature of Long Range Interactions: Role of Disorder
• Electric field fluctuations in the two-dimensional Coulomb fluid
• Neutron-rich nuclei and the equation of state of stellar matter
• A plausible mechanism of muscle stabilization in stall conditions
• Expansion into the vacuum of stochastic gases with long-range interactions
• Long-range interacting systems and the Gibbs-Duhem equation
• Out-of-equilibrium dynamics in systems with long-range interactions: characterizing quasi-stationary states
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
• Non-mean-field effects in systems with long-range forces in competition
• Macroscopic fluctuation theory of interacting Brownian particles
• Quasi-equilibrium nonadditivity
• Lattice Gas Models with Long Range Interactions
• Relaxation dynamics in a long-range system with mixed Hamiltonian and non-Hamiltonian interactions
• On the Conditions for a Quantum Violent Relaxation
• Quantum Coulomb systems : screening, recombination and van der Waals forces
• Unconditional energy dissipation and error estimates of the SAV Fourier spectral method for nonlinear fractional generalized wave equation
• Mixed phases in feedback Ising models
• Hard-core collisional dynamics in the hamiltonian mean-field model
• The internal energy expression of a long-range interaction complex system and its statistical physical properties
• Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$
• Floquet Recurrences in the Double Kicked Top
• Time Parametrizations in Long-Range Interacting Bose-Einstein Condensates
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• The curious spectra and dynamics of non-locally finite crystals
• Temperature and conditions for thermalization after canonical quenches
• Reply to 'Comment on "Vortex distribution in a confining potential"
• Predicting the Final Stationary State of Sheared 2D Euler Fluids
• Generalised Gibbs Ensemble for spherically constrained harmonic models
• Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions
• Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation
• Stability in microcanonical many-body spin glasses
• Enhancement of magnetic anisotropy barrier in long range interacting spin systems
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
• Apparent bistability from weak long-range interactions
• Analysis of the finite-size effect of the long-range Ising model under Glauber dynamics
• A solvable problem in statistical mechanics: the dipole-type Hamiltonian mean field model
• Thermodynamics of spherically symmetric thin-shell spacetimes
• On the origin of Phase Transitions in the absence of Symmetry-Breaking
• Scalability of 3D-DFT by block tensor-matrix multiplication on the JUWELS Cluster
• Dynamics and Thermodynamics of the mean field d-HMF model out-of-equilibrium
• Nondivergent and negative susceptibilities around critical points of a long-range Hamiltonian system with two order parameters
• Fast collective oscillations and clustering phenomena in an antiferromagnetic mean-field model
• Thermodynamics and phase transitions of black holes in contact with a gravitating heat bath