 00230 Alexander, K. S.
 The Spectral Gap of the 2D Stochastic Ising Model with Nearly SingleSpin
Boundary Conditions
(77K, AMSLATeX 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 allplus boundary condition.
Our results are valid at all subcritical temperatures.
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