Finite-time dynamical phase transition in non-equilibrium relaxation

TL;DR

This paper reveals a finite-time dynamical phase transition in a mean-field magnetic model, characterized by a cusp in magnetization distribution at a critical time, with a theoretical framework applicable to similar systems.

Contribution

It introduces a dynamical Landau theory for finite-time phase transitions and establishes an exact mapping to equilibrium transitions, revealing mean-field critical exponents.

Findings

Identification of a cusp singularity in magnetization distribution

Derivation of a dynamical Landau theory for the transition

Mapping between dynamical and equilibrium phase transitions

Abstract

We uncover a finite-time dynamical phase transition in the thermal relaxation of a mean-field magnetic model. The phase transition manifests itself as a cusp singularity in the probability distribution of the magnetisation that forms at a critical time. The transition is due to a sudden switch in the dynamics, characterised by a dynamical order parameter. We derive a dynamical Landau theory for the transition that applies to a range of systems with scalar, parity-invariant order parameters. Close to criticalilty, our theory reveals an exact mapping between the dynamical and equilibrium phase transitions of the magnetic model, and implies critical exponents of mean-field type. We argue that interactions between nearby saddle points, neglected at the mean-field level, may lead to critical, spatiotemporal fluctuations of the order parameter, and thus give rise to novel, dynamical critical phenomena.