Slow relaxation of 2-D stochastic Ising model with random and non-random boundary condition

Abstract We consider finite volume stochastic Ising models corresponding to the usual Ising ferromagnet at sufficiently low temperature, with zero external magnetic field. We show that for a certain class of boundary conditions in which neither (+) nor (-) predominates the other, the spectral gap on a square shrinks exponentially fast in the side-length. We also discuss some consequences of this estimate, including an application to random (1/2-Bernoulli, for example) boundary conditions.