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

Abstract

We present a comprehensive study of phase transitions in single-field systems that relax to a nonequilibrium 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 in the manner of Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise interpretation (e.g., Itô vs Stratonovich) 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.