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Estimates of logarithmic Sobolev constat for finite-volume continuous spin systems (1996)

Wang, Feng-Yu

Springer

Journal of statistical physics 84 (1996), S. 277-293

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ISSN: 1572-9613

Keywords: Logarothmic Sobolev constant ; spectral gap ; stochastic Ising model ; diffusion process ; Peierl's contour ; Gibbs state

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract LetM be a compact, connected Riemannian manifold (with or without boundary); we study the logarithmic Sobolev constant for stochastic Ising models on $$M^{Z^d } $$ . Let {λ} 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 |Δ|(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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02179587

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