00-327 Kenneth S. Alexander, Nobuo Yoshida

The spectral gap of the 2-D stochastic Ising model with mixed boundary conditions (67K, LaTeX) 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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