Communications in Mathematical Physics

, Volume 232, Issue 2, pp 279–302 | Cite as

Einstein Relation for a Class of Interface Models

  • Roberto H. Schonmann


 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 \(\) 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: \(\), where β is the inverse temperature.


Interface Model Einstein Relation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Roberto H. Schonmann
    • 1
  1. 1.Department of Mathematics, UCLA, Los Angeles, CA 90095, USA. E-mail: rhs@math.ucla.eduUS

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