Dynamic Phase Transition and Hysteresis in Kinetic Ising Models

TL;DR

This paper investigates the dynamic phase transition and hysteresis in a kinetic Ising model under oscillating fields, using Monte Carlo simulations to analyze critical behavior and universality class.

Contribution

It provides the first extensive Monte Carlo analysis of the nonequilibrium dynamic phase transition in a kinetic Ising model, estimating critical exponents and exploring universality.

Findings

Critical exponents match the 2D equilibrium Ising universality class.

The transition is inconsistent with 2D random percolation.

Universality class of the nonequilibrium transition remains unresolved.

Abstract

We briefly introduce hysteresis in spatially extended systems and the dynamic phase transition observed as the frequency of the oscillating field increases beyond a critical value. Hysteresis and the decay of metastable phases are closely related phenomena, and a dynamic phase transition can occur only for field amplitudes, temperatures, and system sizes at which the metastable phase decays through nucleation and growth of many droplets. We present preliminary results from extensive Monte Carlo simulations of a two-dimensional kinetic Ising model in a square-wave oscillating field and estimate critical exponents by finite-size scaling techniques adapted from equilibrium critical phenomena. The estimates are consistent with the universality class of the two-dimensional equilibrium Ising model and inconsistent with two-dimensional random percolation. However, we are not aware of any theoretical arguments indicating why this should be so. Thus, the question of the universality class of this nonequilibrium critical phenomenon remains open.