Global Speed Limit for Finite-Time Dynamical Phase Transition and Nonequilibrium Relaxation

TL;DR

This paper demonstrates the existence of finite-time dynamical phase transitions in finite-range Ising models and reveals non-trivial speed limits for relaxation, contrasting with mean field predictions and highlighting the role of local correlations.

Contribution

It extends the understanding of dynamical phase transitions from mean field models to finite-range systems using simulations and analytical methods, revealing new speed limits.

Findings

Dynamical phase transition exists in finite-range Ising models.

Non-trivial speed limits govern the relaxation dynamics.

Local correlations induce kinetic constraints absent in mean field models.

Abstract

Recent works unraveled an intriguing finite-time dynamical phase transition in the thermal relaxation of the mean field Curie-Weiss model. The phase transition reflects a sudden switch in the dynamics. Its existence in systems with a finite range of interaction, however, remained unclear. Here we demonstrate the dynamical phase transition for nearest-neighbor Ising systems on the square and Bethe lattices through extensive computer simulations and by analytical results. Combining large-deviation techniques and Bethe-Guggenheim theory we prove the existence of the dynamical phase transition for arbitrary quenches, including those within the two-phase region. Strikingly, for any given initial condition we prove and explain the existence of non-trivial speed limits for the dynamical phase transition and the relaxation of magnetization, which are fully corroborated by simulations of the microscopic Ising model but are absent in the mean field setting. Pair correlations, which are neglected in mean field theory and trivial in the Curie-Weiss model, account for kinetic constraints due to frustrated local configurations that give rise to a global speed limit.