The randomly driven Ising ferromagnet, Part II: One and two dimensions

TL;DR

This paper investigates the behavior of a one-dimensional Ising ferromagnet under a rapidly changing random external field, comparing theoretical predictions with Monte Carlo simulations to understand fluctuation effects.

Contribution

It extends the analysis of randomly driven Ising models to one dimension, providing partial solutions and simulation results that validate mean field predictions.

Findings

Mean field theory features persist despite strong fluctuations.

Monte Carlo simulations support theoretical predictions.

Partial solutions for one-dimensional case are obtained.

Abstract

We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. In Part I, we introduced a general formalism for describing such systems and presented the mean field theory. In this article we derive results for the one dimensional case, which can be only partially solved. Monte Carlo simulations performed on a square lattice indicate that the main features of the mean field theory survive the presence of strong fluctuations.