We establish upper bounds for the spectral gap of the stochastic Ising modelat low temperature in an N-by-N box, with boundary conditions which are``plus'' except for small regions at the corners which are either free or``minus.'' The spectral gap decreases exponentially in the size of the cornerregions, when these regions are of size at least of order \log N. This meansthat removing as few as O(\log N) plus spins from the corners produces aspectral gap far smaller than the order N^{-2} gap believed to hold under theall-plus boundary condition. Our results are valid at all subcriticaltemperatures.
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