Temperature dependence of the dynamics of random interfaces

Abstract

We study the effects of thermal-noise-induced roughening on the dynamical evolution of random interfaces. This is done using the Allen-Cahn equation with noise, which is appropriate for a system with a nonconserved order parameter. The proportionality constant in the characteristic growth law of domains is renormalized by a temperature-dependent factor. Two different initial configurations are considered. Firstly, a random configuration of interfaces in $d$ dimensions is analyzed using the linearization scheme of Ohta, Jasnow, and Kawasaki. The results suggest that the linearization breaks down at high temperatures; theoretical predictions for low and intermediate temperatures could be tested experimentally. Secondly, a two-dimensional circular domain is analyzed to first order in a low-temperature perturbation series. This is done in the manner of Safran, Sahni, and Grest. However, we obtain results which differ from those of Safran et al. Our results are consistent with those we obtain for the random configuration of interfaces.