Random fields at a nonequilibrium phase transition

TL;DR

This paper shows that in a one-dimensional nonequilibrium system, the phase transition persists despite random-field disorder, with dynamics characterized by ultraslow Sinai walk behavior, contrasting with equilibrium systems.

Contribution

It demonstrates the robustness of the nonequilibrium phase transition against random-field disorder in one dimension, supported by large-scale simulations.

Findings

Phase transition persists in 1D with random-field disorder

Symmetry-broken phase exhibits ultraslow Sinai walk dynamics

Monte-Carlo simulations confirm theoretical predictions

Abstract

We investigate nonequilibrium phase transitions in the presence of disorder that locally breaks the symmetry between two equivalent macroscopic states. In low-dimensional equilibrium systems, such "random-field" disorder is known to have dramatic effects: It prevents spontaneous symmetry breaking and completely destroys the phase transition. In contrast, we demonstrate that the phase transition of the one-dimensional generalized contact process persists in the presence of random field disorder. The dynamics in the symmetry-broken phase becomes ultraslow and is described by a Sinai walk of the domain walls between two different absorbing states. We discuss the generality and limitations of our theory, and we illustrate our results by means of large-scale Monte-Carlo simulations.