The Spectral Gap of the 2-D Stochastic Ising Model with Mixed Boundary Conditions |
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Authors: | Kenneth S Alexander Nobuo Yoshida |
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Institution: | (1) Department of Mathematics, University of Southern California, Los Angeles, California, 90089-1113;(2) Division of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan |
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Abstract: | We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an l×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 l, where <1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on ), the spectral gap decreases exponentially in l. |
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Keywords: | stochastic Ising model spectral gap Glauber dynamics |
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