Critical dynamics of phase transition driven by dichotomous Markov noise

TL;DR

This paper investigates how a dichotomous Markov noise influences the critical dynamics of an Ising spin system, revealing a transition between symmetry-restoring and symmetry-breaking behaviors and analyzing the system's temporal properties.

Contribution

It provides a combined numerical and theoretical analysis of the phase transition driven by dichotomous noise, including a phenomenological model that matches simulation results.

Findings

Identification of a transition between two dynamic regimes

Existence of channels where the order parameter remains for long durations

Good agreement between phenomenological analysis and numerical simulations

Abstract

An Ising spin system under the critical temperature driven by a dichotomous Markov noise (magnetic field) with a finite correlation time is studied both numerically and theoretically. The order parameter exhibits a transition between two kinds of qualitatively different dynamics, symmetry-restoring and symmetry-breaking motions, as the noise intensity is changed. There exist regions called channels where the order parameter stays for a long time slightly above its critical noise intensity. Developing a phenomenological analysis of the dynamics, we investigate the distribution of the passage time through the channels and the power spectrum of the order parameter evolution. The results based on the phenomenological analysis turn out to be in quite good agreement with those of the numerical simulation.