Diffusive scaling of the spectral gap for the dilute Ising lattice-gas dynamics below the percolation threshold

• 成果类型: Article
• 署名作者: Cancrini, N; Martinelli, F
• 署名单位: Consiglio Nazionale delle Ricerche (CNR); Istituto Nazionale per la Fisica della Materia (INFM-CNR); Sapienza University Rome; University of L'Aquila; Roma Tre University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/PL00008790
• 发表日期: 2001
• 页码: 497-534
• 关键词: logarithmic sobolev inequality; equilibrium; relaxation

摘要

We consider a conservative stochastic lattice-gas dynamics reversible with respect to the canonical Gibbs measure of the bond dilute Ising model on Z(d) at inverse temperature beta. When the bond dilution density p is below the percolation threshold we prove that for any particle density and any beta, with probability one, the spectral gap of the generator of the dynamics in a box of side L centered at the origin scales like L-2. Such an estimate is then used to prove a decay to equilibrium for local functions of the form 1/t(alpha-epsilon) where epsilon is positive and arbitrarily small and alpha = 1/2 for d = 1, alpha = I for d greater than or equal to 2. In particular our result shows that, contrary to what happens for the Glauber dynamics, there is no dynamical phase transition when beta crosses the critical value beta (c) of the pure system.