Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model

Abstract

We study the fluctuations of time-additive random observables in the stochastic dynamics of a system of $N$ non-interacting Ising spins. We mainly consider the case of all-to-all dynamics where transitions are possible between any two spin configurations with uniform rates. We show that the cumulant generating function of the time-integral of a normally distributed quenched random function of configurations, i.e., the energy function of the random energy model (REM), has a phase transition in the large $N$ limit for trajectories of any time extent. We prove this by determining the exact limit of the scaled cumulant generating function. This is accomplished by connecting the dynamical problem to a spectral analysis of the all-to-all quantum REM. We also discuss finite $N$ corrections as observed in numerical simulations.

References in corpus (12)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• A minimal model of dynamical phase transition
• Dynamics of measured many-body quantum chaotic systems
• Stability of the quantum Sherrington-Kirkpatrick spin glass model
• Existence of replica-symmetry breaking in quantum glasses
• The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses
• Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model

Cited by in corpus (1)

• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model