The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 22, Number 3 (2012), 1136-1166.
Mixing time for the solid-on-solid model
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.
Ann. Appl. Probab., Volume 22, Number 3 (2012), 1136-1166.
First available in Project Euclid: 18 May 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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