Scaling of fluctuations in one-dimensional interface and hopping models

Abstract

We study time-dependent correlation functions in a family of one-dimensional biased stochastic lattice-gas models in which particles can move up to k lattice spacings. In terms of equivalent interface models, the family interpolates between the low-noise Ising (k=1) and Toom (k=∞) interfaces on a square lattice. Since the continuum description of density (or height) fluctuations in these models involves at most (k+1)th-order terms in a gradient expansion, we can test specific renormalization-group predictions using Monte Carlo methods to probe scaling behavior. In particular we confirm the existence of multiplicative logarithms in the temporal behavior of mean-squared height fluctuations [∼t^½(ln t)^¼], induced by a marginal cubic gradient term. Analogs of redundant operators, familiar in the context of equilibrium systems, also appear to occur in these nonequilibrium systems.