Estimates of logarithmic Sobolev constant for finite-volume continuous spin systems
Journal Article
·
· Journal of Statistical Physics
- Beijing Normal Univ. (China)
Let M be a compact, connected Riemannian manifold (with or without boundary); we study the logarithmic Sobolev constant for stochastic Ising models on M{sup Zd}. Let ({Lambda}) be a sequence of cubes in Z{sup d}, we show that the logarithmic Sobolev constant for the finite systems on M{sup {Lambda}} shrinks at most exponentially fast in {vert_bar}{Lambda}{vert_bar}{sup (d-1)/d} (d{ge}2), which is sharp in order for the classical Ising models with M = [-1, 1]. Moreover, a geometrical lemma proved by L.E. Thomas is also improved.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 469006
- Journal Information:
- Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1-2 Vol. 84; ISSN JSTPBS; ISSN 0022-4715
- Country of Publication:
- United States
- Language:
- English
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