02-190 Roberto H. Schonmann

Einstein relation for a class of interface models (319K, ps) Apr 18, 02

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Abstract. A class of SOS interface models which can be seen as simplified stochastic Ising model interfaces is studied. In the absence of an external field the long-time fluctuations of the interface are shown to behave as Brownian motion with diffusion coefficient $(\sigma^{\text{GK}})^2$ given by a Green-Kubo formula. When a small external field $h$ is applied, it is shown that the shape of the interface converges exponentially fast to a stationary distribution and the interface moves with an asymptotic velocity $v(h)$. The mobility is shown to exist and to satisfy the Einstein relation: $(dv/dh)(0) = \beta (\sigma^{\text{GK}})^2$, where $\beta$ is the inverse temperature.

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