The randomly driven Ising ferromagnet, Part I: General formalism and mean field theory

TL;DR

This paper develops a mean-field theory for a randomly driven Ising ferromagnet under Glauber dynamics, revealing a novel first-order phase transition and complex non-equilibrium stationary states with fractal structures.

Contribution

It introduces a general formalism for such systems and uncovers a new type of phase transition related to symmetry breaking and dynamic freezing.

Findings

Discovery of a first-order phase transition in the system

Identification of complex stationary states with fractal support

Demonstration of parameter-dependent transition from singular to continuous distributions

Abstract

We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. After introducing a general formalism for describing such systems, we consider here the mean-field theory. A novel type of first order phase transition related to spontaneous symmetry breaking and dynamic freezing is found. The non-equilibrium stationary state has a complex structure, which changes as a function of parameters from a singular-continuous distribution with Euclidean or fractal support to an absolutely continuous one.