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