Journal of Statistical Physics, Vol. 104, Nos. 1/2, 2001, p. 89-109.
We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an lxl box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length l in the boundary is bounded by delta*l, where delta < 1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on delta), the pectral gap decreases exponentially in l.