Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model

Abstract

We study the non-equilibrium relaxation of the spherical spin-glass model with p-spin interactions in the $N\to \infty$ limit. We analytically solve the asymptotics of the magnetization and the correlation and response functions for long but finite times. Even in the thermodynamic limit the system exhibits `weak' (as well as `true') ergodicity breaking and aging effects. We determine a functional Parisi-like order parameter $P_d(q)$ which plays a similar role for the dynamics to that played by the usual function for the statics.

8 pages, Roma preprint

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• Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Zero-th law in structural glasses: an example
• Accelerating, to some extent, the $p$-spin dynamics
• Non-equilibrium structures and slow dynamics in a two dimensional spin system with competitive long range and short range interactions
• Dynamics for spherical spin glasses: disorder dependent initial conditions
• Coupling between aging and convective motion in a colloidal glass of Laponite
• An Analytical Theory of Curriculum Learning in Teacher-Student Networks
• Fluctuation-dissipation relations and energy landscape in an out-of-equilibrium strong glass-forming liquid
• Off equilibrium fluctuations in a polymer glass
• Exactly Solvable Model Glass with a Facilitated Dynamics
• Spin-glass dynamics: experiment, theory and simulation
• Diffusion in disordered media as a process with memory
• Local overlaps, heterogeneities and the local fluctuation dissipation relations
• Avalanches and hysteresis in frustrated superconductors and XY-spin-glasses
• Off-Equilibrium Dynamics of a 4D Spin Glass with Asymmetric Couplings
• Asymmetric Langevin dynamics for the ferromagnetic spherical model
• Localization in the Discrete Non-Linear Schrödinger Equation and geometric properties of the microcanonical surface
• Thresholds of descending algorithms in inference problems
• Regge theory and statistical mechanics
• A note on weakly discontinuous dynamical transitions
• Role of initial conditions in the dynamics of quantum glassy systems
• PDE/statistical mechanics duality: relation between Guerra's interpolated $p$-spin ferromagnets and the Burgers hierarchy
• Extremal driving as a mechanism for generating long-term memory
• On the superposition principle and non-linear response in spin glasses
• Universality of REM-like aging in mean field spin glasses
• The Complexity of Vector Spin Glasses
• Probing chaos in the spherical p-spin glass model
• Aging, memory and rejuvenation: some lessons from simple models
• Fluctuations of two-time quantities and non-linear response functions
• From particles to spins: Eulerian formulation of supercooled liquids and glasses
• Off equilibrium dynamics of the Frustrated Ising Lattice Gas
• Nonequilibrium dynamics in an amorphous solid
• Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations
• Spin Glass Theory: numerical and experimental results in three-dimensional systems
• Dynamics and thermodynamics of the spherical frustrated Blume-Emery-Griffiths model
• A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models
• Observable Dependent Quasi-Equilibrium in Slow Dynamics
• Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature
• Bringing together two paradigms of non-equilibrium: Fragile versus robust aging in driven glassy systems
• Dynamics of an Ising Spin Glass on the Bethe Lattice
• Quasi-equilibrium during aging of the 2D Edwards-Anderson model
• Damage spreading transition in glasses: a probe for the ruggedness of the configurational landscape
• How to escape atypical regions in the symmetric binary perceptron: a journey through connected-solutions states
• Competition between Barrier- and Entropy-Driven Activation in Glasses
• Dynamic Gardner crossover in a simple structural glass
• Precursors of the Spin Glass Transition in Three Dimensions
• Structural relaxation, dynamical arrest and aging in soft-sphere liquids
• Numerical renormalization of glassy dynamics
• Testing replica predictions in experiments
• Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics
• Counting equilibria of large complex systems by instability index
• Short-time dynamics in the 1D long-range Potts model
• Instantaneous normal modes of glass-forming liquids during the athermal relaxation process of the steepest descent algorithm
• High-dimensional Asymptotics of Langevin Dynamics in Spiked Matrix Models
• Effective temperatures for single particle system under dichotomous noise
• Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures
• Langevin dynamics of the Lebowitz-Percus model
• Quantitative investigation of the mean-field scenario for the structural glass transition from a schematic mode-coupling analysis of experimental data
• Trap models with slowly decorrelating observables
• Condensation and equilibration in an urn model
• Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models
• Role of free energy landscape in the dynamics of mean field glassy systems
• Equilibrium statistics of a slave estimator in Langevin processes
• Ginzburg-Landau theory of the cluster glass phase
• Heat exchanges in coarsening systems
• Thermodynamics of the Fredrickson-Andersen Model on the Bethe Lattice
• Kinetically driven glassy transition in an exactly solvable toy model with reversible mode coupling mechanism and trivial statics
• Quasi equilibrium construction for the long time limit of glassy dynamics
• Damage spreading in the mode-coupling equations for glasses
• Dynamics of structural models with a long-range interaction: glassy versus non-glassy behavior
• Growth Kinetics and Aging Phenomena in a Frustrated System
• Irreversibility in Non-reciprocal Chaotic Systems
• The Sherrington-Kirkpatrick model for spin glasses: A new approach for the solution
• Probing the Fluctuation-Dissipation Theorem in a Perrin-like Experiment
• Out-of-equilibrium thermodynamic relations in systems with aging and slow relaxation
• Clever algorithms for glasses work by time reparametrization
• A constrained TAP approach for disordered spin models: application to the mixed spherical case
• Glass transition in models with controlled frustration
• The effect of quantum fluctuations on the coloring of random graphs
• Statistical Mechanics of a Two-Dimensional System with Long Range Interaction
• Stochastic Gradient Descent-like relaxation is equivalent to Metropolis dynamics in discrete optimization and inference problems
• Maximum-energy records in glassy energy landscapes
• Effects from Additional Random Configuration to Linear Response and Modified Fluctuation-Dissipation Relation
• Supersymmetry approach in the field theory of ergodicity breaking transitions
• Relaxation dynamics of the three-dimensional Coulomb Glass model
• Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
• Large time effective kinetics $\beta$-functions for quantum (2+p)-spin glass
• Differentiability of the speed of biased random walks on Galton-Watson trees
• Embedding a Native State into a Random Heteropolymer Model: The Dynamic Approach
• Self-Sustained Clusters as Drivers of Computational Hardness in $p$-spin Models
• How glasses explore configuration space
• Packing hard spheres with short-range attraction in infinite dimension: Phase structure and algorithmic implications
• The glass susceptibility: growth kinetics and saturation under shear
• Dynamic phase diagram of the Number Partitioning Problem
• Free energy barriers in the Sherrington-Kirkpatrick model
• A pedagogical introduction to the replica method for fragile glasses
• Out of equilibrium dynamics of the toy model with mode coupling and trivial Hamiltonian
• Off-equilibrium dynamics in the energy landscape of a simple model glass
• Coarsening on percolation clusters: out-of-equilibrium dynamics versus non linear response
• The effect of screening on the relaxation dynamics in the Coulomb glass
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Slow nonequilibrium dynamics: parallels between classical and quantum glasses and gently driven systems
• Effects of Frustration on Fluctuation-dissipation Relations
• Wehrl Entropy and Entanglement Complexity of Quantum Spin Systems
• The quantum $p$-spin glass model: A user manual for holographers
• Real-space model for activated processes in rejuvenation and memory behavior of glassy systems
• Comment on "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$"
• Inevitable Irreversibility Generated by the Glass Transition of the Binary Lattice Gas Model
• High-Temperature Dynamics of Spin Glasses
• Spin-glass model with partially annealed asymmetric bonds
• Rank-one matrix estimation: analytic time evolution of gradient descent dynamics
• Ergodicity breaking of an inorganic glass in aging near $T_g$ probed by elasticity relaxation
• Analytical Study of Momentum-Based Acceleration Methods in Paradigmatic High-Dimensional Non-Convex Problems
• Stochastic melonic kinetics with random initial conditions
• The rejuvenation effect in the two-state random energy model
• Who is Afraid of Big Bad Minima? Analysis of Gradient-Flow in a Spiked Matrix-Tensor Model
• Dynamical fluctuations in an exactly solvable model of spin glasses
• Physics of glassy systems
• Classical and Quantum Behavior in Mean-Field Glassy Systems
• Controlling the Glass Transition through Active Fluctuating Interactions
• Decoherence in a nonequilibrium environment
• Dynamical arrest with zero complexity: the unusual behavior of the spherical Blume Emery Griffiths disordered model
• Rare Trajectories in a Prototypical Mean-field Disordered Model: Insights into Landscape and Instantons
• Functional Renormalization Group Approach for Signal Detection
• Strong ergodicity breaking in dynamical mean-field equations for mixed p-spin glasses
• Off Equilibrium Study of the Fluctuation-Dissipation Relation in the Easy-Axis Heisenberg Antiferromagnet on the Kagome Lattice
• Time-Varying Energy Landscapes and Temperature paths: Dynamic Transition Rates in locally Ultrametric Complex Systems
• A consequence of local equilibration and heterogeneity in glassy materials
• Aging of the Nonlinear Optical Susceptibility of colloidal solutions
• Dynamical critical behavior on the Nishimori point of frustrated Ising models
• Logarithmic critical slowing down in complex systems: from statics to dynamics
• Fluctuation Distributions of Energy Minima in Complex Landscapes
• Biased thermodynamics can explain the behaviour of smart optimization algorithms that work above the dynamical threshold
• Singular perturbation near mode-coupling transition
• Distribution of Attraction Basins in a Family of Simple Glasses
• Ubiquitous Dynamical Time Asymmetry in Measurements on Materials and Biological Systems
• Non-equilibrium fluctuation dissipation relations in binary glasses
• Slow dynamics of glassy systems
• Complexity as the driving force for glassy transitions
• Emergent Thermalization Thresholds in Unitary Dynamics of Inhomogeneously Disordered Quantum Systems
• Starvation suppression in dense scale-free metabolic networks: Dynamical mean-field analysis of catalytic reaction networks
• Sachdev-Ye-Kitaev Model in a Quantum Glassy Landscape
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain
• Generalized Khinchin Theorem for a Class of Aging Processes
• Gradient descent dynamics and the jamming transition in infinite dimensions
• Replica symmetry breaking in long-range glass models without quenched disorder
• Searching for emergent spacetime in spin glasses
• Sustaining supercooled mixed phase via resonant oscillations of the order parameter
• Derivation of the spin-glass order parameter from stochastic thermodynamics
• Dynamics of soft interacting particles on a comb
• Local energy approach to the dynamic glass transition
• Ma-Dasgupta renormalization studies of various disordered systems
• On the Static and Dynamical Transition in the Mean-Field Potts Glass
• Thermal noise properties of two aging materials