Dynamics of an anchored Toom interface

At a sufficiently low noise level the two-dimensional Toom model (North East Center majority vote with small errors) has two stationary states. The authors study the statistical properties of interfaces between these phases, with particular attention to a stationary interface maintained in the third quadrant by mixed +- boundary conditions. The fluctuations in this interface are found numerically to be much smaller than in equilibrium interfaces; they have exponents 1/4 or 1/3, depending on the symmetry, rather than 1/2. The correlations exhibit long-range behaviour reminiscent of self-organized criticality. They construct several approximate theories of the interface which reproduce this behaviour, at least qualitatively. The most accurate of these leads to a novel nonlinear partial differential equation for the asymptotic probability distribution of the fluctuations along the interface.