Dynamics of field-driven interfaces in the two-dimensional Ising model

Abstract

The time-dependent properties of an inclined interface separating up and down spin regions in a two-dimensional nearest-neighbour Ising model evolving under Glauber dynamics in a non-zero field are studied. In the limit of large exchange coupling, the model reduces to the single-step model for ballistic growth and thence to the asymmetric exclusion process which describes a driven diffusive system of hard core particles on a one-dimensional lattice. The drift velocity of the interface is found as a function of field, temperature and inclination, and interface correlation functions are related to sliding tag correlation functions in the particle system. The existence of a critical value of the sliding-tag velocity implies that there is an inclination-dependent easy direction along which temporal interface fluctuations grow subdiffusively. This direction is found, as is the asymptotic behaviour of the correlation function in all other directions.