Generic nonergodic behavior in locally interacting continuous systems

Abstract

Certain probabilistic cellular automata (PCA) have been shown to exhibit nonergodic behavior (i.e., possess two or more distinct stable states) over finite regions of their parameter spaces, i.e., generically. To demonstrate that this behavior is a consequence of irreversible (or ``nonequilibrium'') dynamics and not special to the discrete space, time, and variables of PCA, we define and study a class of noisy partial differential equations (Langevin models), which are constructed to have spatially anisotropic domain-wall kinetics. The models are simple nonequilibrium generalizations of ordinary equilibrium time-dependent Ginzburg-Landau theories. We present analytic and numerical arguments to show that these models exhibit the same generic nonergodic behavior as do their discrete PCA counterparts.