Freezing in stripe states for kinetic Ising models: a comparative study of three dynamics

TL;DR

This study compares how an Ising ferromagnet on a square lattice evolves under three different zero-temperature dynamics, examining the applicability of critical percolation predictions across these dynamics, including reversible and irreversible limits.

Contribution

It introduces a comparative analysis of three zero-temperature dynamics for the kinetic Ising model, highlighting differences in freezing behavior and the relevance of critical percolation predictions.

Findings

Critical percolation predictions hold for Glauber dynamics.

Differences observed in freezing behavior between reversible and irreversible dynamics.

Irreversible dynamics show distinct patterns in reaching ground or metastable states.

Abstract

We present a comparative study of the fate of an Ising ferromagnet on the square lattice with periodic boundary conditions evolving under three different zero-temperature dynamics. The first one is Glauber dynamics, the two other dynamics correspond to two limits of the directed Ising model, defined by rules that break the full symmetry of the former, yet sharing the same Boltzmann-Gibbs distribution at stationarity. In one of these limits the directed Ising model is reversible, in the other one it is irreversible. For the kinetic Ising-Glauber model, several recent studies have demonstrated the role of critical percolation to predict the probabilities for the system to reach the ground state or to fall in a metastable state. We investigate to what extent the predictions coming from critical percolation still apply to the two other dynamics.