Stochastic field effects in a two-state system: symmetry breaking and symmetry restoring

TL;DR

This study investigates the effects of a time-varying Gaussian random magnetic field on the Ising model, revealing three distinct phases and novel noise-induced transitions with unique characteristics.

Contribution

It introduces a detailed analysis of soft phases and identifies a non-conventional discontinuous transition characterized by diverging escape times.

Findings

Identified three phases: soft-paramagnetic, soft-ferromagnetic, and ferromagnetic.

Discovered a noise-induced transition at the critical temperature of the field-free model.

Observed a discontinuous transition with diverging escape times, not fitting traditional first-order classification.

Abstract

We study the Ising model under a time-varying, but spatially homogeneous, Gaussian random magnetic field. In the Monte Carlo simulations, we go beyond the standard analysis of the order parameter by measuring the magnetization probability distribution as a function of temperature and field strength, and by computing the time required for the system to escape from a completely ordered state of the magnetization. We identify three distinct phases: a soft-paramagnetic phase, a soft-ferromagnetic phase and a bona-fide ferromagnetic phase. These soft phases display broad magnetization distributions that tend to limiting forms that remain finite in both height and width in the thermodynamic limit. The transition between the soft-paramagnetic and soft-ferromagnetic phases is a noise-induced transition and, for small field amplitudes, occurs at the critical temperature of the field-free Ising model. The transition from the soft-ferromagnetic to the ferromagnetic phase occurs at lower temperatures and is discontinuous, yet it does not fall into the conventional first-order class. Instead, it is characterized by a diverging escape time from an ordered magnetization state.