The Stochastic Ising Model with the Mixed Boundary Conditions

We estimate the spectral gap of the two-dimensional stochastic Ising model for four classes of mixed boundary conditions. On a finite square, in the absence of an external field, two-sided estimates on the spectral gap for the first class of (weak positive) boundary conditions are given. Further, at inverse temperatures β>βc, we will show lower bounds of the spectral gap of the Ising model for the other three classes mixed boundary conditions