Scaling of fluctuations in one-dimensional interface and hopping models.

We study time-dependent correlation functions in a family of one-dimensional biased stochastic lattice-gas models in which particles can move up to [ital k] lattice spacings. In terms of equivalent interface models, the family interpolates between the low-noise Ising ([ital k]=1) and Toom ([ital k]=[infinity]) interfaces on a square lattice. Since the continuum description of density (or height) fluctuations in these models involves at most ([ital 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 [[similar to][ital t][sup 1/2](ln [ital t])[sup 1/4]], 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.