The Annals of Applied Probability

Mixing time for the solid-on-solid model

Fabio Martinelli and Alistair Sinclair

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Abstract

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 Õ(n3.5), which is tight within a factor of Õ(√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.

Article information

Source
Ann. Appl. Probab., Volume 22, Number 3 (2012), 1136-1166.

Dates
First available in Project Euclid: 18 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1337347541

Digital Object Identifier
doi:10.1214/11-AAP791

Mathematical Reviews number (MathSciNet)
MR2977988

Zentralblatt MATH identifier
1283.60122

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs

Keywords
Solid-on-solid model Markov chain Monte Carlo censoring Glauber dynamics mixing time monotonicity Ising model

Citation

Martinelli, Fabio; Sinclair, Alistair. Mixing time for the solid-on-solid model. Ann. Appl. Probab. 22 (2012), no. 3, 1136--1166. doi:10.1214/11-AAP791. https://projecteuclid.org/euclid.aoap/1337347541


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