The spectral gap of the 2-D stochastic Ising model with mixed boundary conditions

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We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an n-by-n 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 n in the boundary is bounded by δn, where δ< 1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on δ), the spectral gap decreases exponentially in n.
18 pages

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Probability, Mathematical Physics, 60K35 (primary), 82C20 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/59803

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0008201
 http://arxiv.org/abs/math/0008201

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arXiv