MIXING TIME FOR THE SOLID-ON-SOLID MODEL

• 成果类型: Article
• 署名作者: Martinelli, Fabio; Sinclair, Alistair
• 署名单位: Roma Tre University; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP791
• 发表日期: 2012
• 页码: 1136-1166
• 关键词: glauber dynamics; markov-chains; statistical-mechanics; boundary-conditions; ising-model; equilibrium; droplet; systems; lattice; graphs

摘要

We analyze the mixing time of a natural local Markov chain (the Glauber dynamics) on configurations of the solid-on-solid model of statistical physics. This model has been proposed, among other things, as an idealization of the behavior of contours in the Ising model at low temperatures. Our main result is an upper bound on the mixing time of (O) over tilde (n(3.5)), which is tight within a factor of (O) over tilde(root n). The proof, which in addition gives some insight into the actual evolution of the contours, requires the introduction of a number of novel analytical techniques that we conjecture will have other applications.