Nonequilibrium phase transitions and stationary state solutions of a three-dimensional random-field Ising model under a time dependent periodic external field

TL;DR

This study investigates the nonequilibrium phase transitions of a three-dimensional kinetic Ising model with randomly oscillating external fields, revealing how different amplitude distributions affect phase diagram features and state coexistence.

Contribution

It introduces a detailed analysis of the dynamic phase behavior of a 3D random-field Ising model under periodic fields using effective field theory and explores the effects of bimodal and trimodal amplitude distributions.

Findings

High frequency phase diagrams resemble pure Ising model.

Coexistence regions depend on amplitude distribution and frequency.

Trimodal distribution can eliminate coexistence regions.

Abstract

Nonequilibrium behavior and dynamic phase transition properties of a kinetic Ising model under the influence of periodically oscillating random-fields have been analyzed within the framework of effective field theory (EFT) based on a decoupling approximation (DA). Dynamic equation of motion has been solved for a simple cubic lattice ($q=6$) by utilizing a Glauber type stochastic process. Amplitude of the sinusoidally oscillating magnetic field is randomly distributed on the lattice sites according to bimodal and trimodal distribution functions. For a bimodal type of amplitude distribution, it is found in the high frequency regime that the dynamic phase diagrams of the system in temperature versus field amplitude plane resemble the corresponding phase diagrams of pure kinetic Ising model. Our numerical results indicate that for a bimodal distribution, both in the low and high frequency regimes, the dynamic phase diagrams always exhibit a coexistence region in which the stationary state (ferro or para) of the system is completely dependent on the initial conditions whereas for a trimodal distribution, coexistence region disappears depending on the values of system parameters.