00-230 Alexander, K. S.

The Spectral Gap of the 2-D Stochastic Ising Model with Nearly Single-Spin Boundary Conditions (77K, AMS-LATeX 1.2) May 18, 00

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Abstract. We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an $N \times N$ 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 corner regions, when these regions are of size at least of order $\log N$. This means that removing as few as $O(\log N)$ plus spins from the corners produces a spectral gap far smaller than the order $N^{-2}$ gap believed to hold under the all-plus boundary condition. Our results are valid at all subcritical temperatures.

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