Abstract
ABSTRACT We present a comprehensive study of phase transitions in single-field extended systems that relax to a non-equilibrium global steady state. The mechanism we focus on is not the so-called Stratonovich drift but is insteadsimilar to the one associated with noise-induced transitions a Ia Horsthemke-Lefever in zero-dimensional systems.As a consequence, the noise interpretation (e.g., Ito vs Stratonovich) merely shifts the phase boundaries. Withthe help of a mean-field approximation, we present a broad qualitative picture of the various phase diagramsthat can be found in these systems.Keywords: Phase transitions, relaxational systems, stochastic processes 1. INTRODUCTION Relaxational models describe the flow of a field co (t) defined on a d-dimensional lattice via a Langevin equationof the form (t) = F6)}) +F112(t). (1) Here i labels a lattice site, F is a positive constant, ({o}) (coi, . . . , coN) denotes the entire set of fields, andare Gaussian white noises with zero mean and correlation functions
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