 00327 Kenneth S. Alexander, Nobuo Yoshida
 The spectral gap of the 2D stochastic Ising model with mixed boundary
conditions
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Aug 29, 00

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Abstract. We establish upper bounds for the spectral gap of the stochastic Ising model
at low temperatures in an $l \times l$ 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 $l$ in the boundary is
bounded by $\delta l$, 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 $l$.
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