Estimates of logarithmic Sobolev constat for finite-volume continuous spin systems |
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Authors: | Feng-Yu Wang |
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Institution: | (1) Department of Mathematics, Beijing Normal University, 100875 Beijing, China |
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Abstract: | LetM be a compact, connected Riemannian manifold (with or without boundary); we study the logarithmic Sobolev constant for stochastic Ising models on
. Let { } be a sequence of cubes inZ
d
; we show that the logarithmic Sobolev constant for the finite systems onM
A
shrinks at most exponentially fast in | |(d-1)/d
(d 2), which is sharp in order for the classical Ising models withM=–1, 1]. Moreover, a geometrical lemma proved by L. E. Thomas is also improved. |
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Keywords: | Logarothmic Sobolev constant spectral gap stochastic Ising model diffusion process Peierl's contour Gibbs state |
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