We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such "random-field" disorder destroys the phase transition in low dimensions by preventing spontaneous symmetry breaking. In contrast, we show here that random-field disorder fails to destroy the nonequilibrium phase transition of the one- and two-dimensional generalized contact process. Instead, it modifies the dynamics in the symmetry-broken phase. Specifically, the dynamics in the one-dimensional case is described by a Sinai walk of the domain walls between two different absorbing states. In the two-dimensional case, we map the dynamics onto that of the well studied low-temperature random-field Ising model. We also study the critical behavior of the nonequilibrium phase transition and characterize its universality class in one dimension. We support our results by large-scale Monte Carlo simulations, and we discuss the applicability of our theory to other systems.



Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Domain Walls; Intelligent Systems; Ising Model; Monte Carlo Methods; Temperature; Absorbing-State Transitions; Critical Behavior; Equilibrium Systems; Low Temperatures; Nonequilibrium Phase Transitions; Random Field Ising Models; Spontaneous Symmetry Breaking; Universality Class; Dynamics

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2016 American Physical Society (APS), All rights reserved.

Publication Date

01 Feb 2016