Comprehensive study of phase transitions in relaxational systems with field-dependent coefficients

TL;DR

This paper investigates phase transitions in single-field relaxational systems with field-dependent coefficients, revealing how noise interpretation affects phase boundaries and providing a comprehensive theoretical and numerical analysis.

Contribution

It introduces a broad mean-field framework for understanding noise-induced phase transitions in non-equilibrium systems with field-dependent coefficients.

Findings

Noise interpretation shifts phase boundaries

Mean-field theory captures diverse phase diagrams

Numerical simulations confirm theoretical predictions

Abstract

We present a comprehensive study of phase transitions in single-field systems that relax to a non-equilibrium global steady state. The mechanism we focus on is not the so-called Stratonovich drift combined with collective effects, but is instead similar to the one associated with noise-induced transitions a la Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise interpretation (e.g., Ito vs Stratonvich) merely shifts the phase boundaries. With the help of a mean-field approximation, we present a broad qualitative picture of the various phase diagrams that can be found in these systems. To complement the theoretical analysis we present numerical simulations that confirm the findings of the mean-field theory.