Trajectory phase transitions in non-interacting spin systems

Abstract

We show that a collection of independent Ising spins evolving stochastically can display surprisingly large fluctuations towards ordered behaviour, as quantified by certain types of time-integrated plaquette observables, despite the underlying dynamics being non-interacting. In the large deviation (LD) regime of long times and large system size, this can give rise to a phase transition in trajectory space. As a non-interacting system we consider a collection of spins undergoing single spin-flip dynamics at infinite-temperature. For the dynamical observables we study, the associated tilted generators have an exact and explicit spin-plaquette duality. Such setup suggests the existence of a transition (in the large size limit) at the self-dual point of the tilted generator. The nature of the LD transition depends on the observable. We consider explicitly two situations: (i) for a pairwise bond observable the LD transition is continuous, and equivalent to that of the transverse field Ising model; (ii) for a higher order plaquette observable, in contrast, the LD transition is first order. Case (i) is easy to prove analytically, while we confirm case (ii) numerically via an efficient trajectory sampling scheme that exploits the non-interacting nature of the original dynamics.

arXiv comment11 pages, 6 figures

References in corpus (46)

• The large deviation approach to statistical mechanics
• Statistically optimal analysis of samples from multiple equilibrium states
• Macroscopic fluctuation theory
• Dynamic first-order phase transition in kinetically constrained models of glasses
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Thermodynamic formalism for systems with Markov dynamics
• Macroscopic current fluctuations in stochastic lattice gases
• Large deviations and ensembles of trajectories in stochastic models
• Distribution of current in non-equilibrium diffusive systems and phase transitions
• Space-time Thermodynamics of the Glass Transition
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Simulating rare events in dynamical processes
• Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Ergodicity and large deviations in physical systems with stochastic dynamics
• Glassy dynamics and aging in an exactly solvable spin model
• Strong-weak coupling self-duality in the two-dimensional quantum phase transition of $p+ip$ superconducting arrays
• Population dynamics method with a multi-canonical feedback control
• Fractal Symmetric Phases of Matter
• Making rare events typical in Markovian open quantum systems
• A minimal model of dynamical phase transition
• Glassiness and constrained dynamics of a short-range non-disordered spin model
• The Lee-Yang theory of equilibrium and nonequilibrium phase transitions
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Large deviation function for entropy production in driven one-dimensional systems
• Exact fluctuations of nonequilibrium steady states from approximate auxiliary dynamics
• Large deviations conditioned on large deviations I: Markov chain and Langevin equation
• Glassiness through the emergence of effective dynamical constraints in interacting systems
• Rare behavior of growth processes via umbrella sampling of trajectories
• Importance sampling large deviations in nonequilibrium steady states. I
• Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit
• Diffusions conditioned on occupation measures
• Large-deviation theory for a Brownian particle on a ring: a WKB approach
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Large deviation function for the entropy production: Optimal trajectory and role of fluctuations
• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• Yang-Lee zeros for a nonequilibrium phase transition
• Sampling rare events across dynamical phase transitions
• Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics
• Large deviations of ergodic counting processes: a statistical mechanics approach
• Transition path sampling algorithm for discrete many-body systems
• Phases of quantum dimers from ensembles of classical stochastic trajectories
• Transition in coupled replicas may not imply a finite temperature ideal glass transition in glass forming systems
• Direct evaluation of dynamical large-deviation rate functions using a variational ansatz
• The boundary effects of transverse field Ising model
• Quantum criticality from Ising model on fractal lattices

Cited by in corpus (15)

• Generalized Symmetries in Condensed Matter
• Construction of Fractal Order and Phase Transition with Rydberg Atoms
• Towards Non-Invertible Anomalies from Generalized Ising Models
• Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model
• Pascal's Triangle Fractal Symmetries
• Beyond the Freshman's Dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lattice models
• Boundary conditions dependence of the phase transition in the quantum Newman-Moore model
• Dynamical phase transitions for the activity biased Ising model in a magnetic field
• A Multicritical Point with Infinite Fractal Symmetries
• Fracton and topological order in the XY checkerboard toric code
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model
• Rejection-free quantum Monte Carlo in continuous time from transition path sampling
• A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains
• Immobile and mobile excitations of three-spin interactions on the diamond chain
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions