The spectral gap of the 2-D stochastic Ising model with nearly single-spin boundary conditions

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dc.creatorAlexander, Kenneth S.
dc.date2000-08-29
dc.date.accessioned2026-07-07T04:37:02Z
dc.date.available2026-07-07T04:37:02Z
dc.descriptionWe establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N-by-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.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0008216
dc.identifierhttp://arxiv.org/abs/math/0008216
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59814
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject82C20 (primary), 60K35 (secondary)
dc.titleThe spectral gap of the 2-D stochastic Ising model with nearly single-spin boundary conditions
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