Open Access
June 2012 Mixing time for the solid-on-solid model
Fabio Martinelli, Alistair Sinclair
Ann. Appl. Probab. 22(3): 1136-1166 (June 2012). DOI: 10.1214/11-AAP791


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.


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Fabio Martinelli. Alistair Sinclair. "Mixing time for the solid-on-solid model." Ann. Appl. Probab. 22 (3) 1136 - 1166, June 2012.


Published: June 2012
First available in Project Euclid: 18 May 2012

zbMATH: 1283.60122
MathSciNet: MR2977988
Digital Object Identifier: 10.1214/11-AAP791

Primary: 60K35
Secondary: 82C20

Keywords: Censoring , Glauber dynamics , Ising model , Markov chain Monte Carlo , mixing time , Monotonicity , Solid-on-solid model

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.22 • No. 3 • June 2012
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