Nonequilibrium Phase Transition To Temporal Oscillations In Mean-Field Spin Models

TL;DR

This paper develops a mean-field theory for nonequilibrium phase transitions to oscillatory states in spin models, introducing a nonequilibrium Landau free energy and Hamiltonian as key order parameters.

Contribution

It presents a novel theoretical framework for analyzing nonequilibrium phase transitions to oscillations, including explicit formulas for the free energy and Hamiltonian from stochastic spin dynamics.

Findings

Identification of a Hamiltonian as the order parameter for oscillations

Explicit derivation of the nonequilibrium Landau free energy

Observation of a replica symmetry breaking-like overlap distribution

Abstract

We propose a mean-field theory for nonequilibrium phase transitions to a periodically oscillating state in spin models. A nonequilibrium generalization of the Landau free energy is obtained from the join distribution of the magnetization and its smoothed stochastic time derivative. The order parameter of the transition is a Hamiltonian, whose nonzero value signals the onset of oscillations. The Hamiltonian and the nonequilibrium Landau free energy are determined explicitly from the stochastic spin dynamics. The oscillating phase is also characterized by a non-trivial overlap distribution reminiscent of a continuous replica symmetry breaking, in spite of the absence of disorder. An illustration is given on an explicit kinetic mean-field spin model.