Dynamics of an anchored Toom interface

Abstract

Abstract. At a sufficiently IOW noise level the two-dimensional Toom model (North East Center majority vote with small errors) has two stationary states. We study the statistical properties of interfaces between these phases, with particular attention lo a stationary interface maintained in the third quadrant by mixed +- boundary conditions. The Auctu-ations in this interface are found numerically to be much smaller than in equilibrium interfaces; they have exponents $ or i, depending on the symmetry, rather than i. The correlations exhibit long-range behaviour reminiscent of self-organized criticality. We constmct several approximate theories of the interface which reproduce this behaviour, at least qualitatively. Thhe most accurate of these leads to a novel nonlinear partial differential equation lor the asymptotic probability distribution of the fluctuations along the interface. Dedicated to Michael Fisher on the occasion of his sixtieth birthday. I.!rtr&!etins There is much current interest in the structure of states of lattice systems obtained as stationary measures for various kinds of stochastic dynamics. These states typically do not correspond to equilibrium Gibbs ensembles with any reasonable interactions.