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

Juan P. Garrahan; Chokri Manai; Simone Warzel

doi:10.1098/rsta.2021.0415

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arXiv · 2205.07487

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

Juan P. Garrahan·Chokri Manai·Simone Warzel

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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.

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Juan P. Garrahan, Chokri Manai, Simone Warzel. 2022-05-16. Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model. https://doi.org/10.1098/rsta.2021.0415

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