The spectral gap of the 2-D stochastic Ising model with mixed boundary   conditions
  We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an n-by-n 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 n in the boundary is bounded by \delta n, where \delta < 1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on \delta), the spectral gap decreases exponentially in n. 
Kenneth S. Alexander (University of Southern California), Nobuo   Yoshida (Kyoto University)