Mixing time for the solid-on-solid model

Authors:
Fabio Martinelli;Alistair Sinclair
Affiliations:
University of Roma Tre, Rome, Italy;University of California, Berkeley, CA, USA
Venue:
Proceedings of the forty-first annual ACM symposium on Theory of computing
Year:
2009

Citing 3
Cited 0

Exact sampling with coupled Markov chains and applications to statistical mechanics

Proceedings of the seventh international conference on Random structures and algorithms
Markov Chain Algorithms for Planar Lattice Structures

SIAM Journal on Computing
The Ising Model on Trees: Boundary Conditions and Mixing Time

FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science

Quantified Score

Hi-index	0.00

Visualization

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 O~(n3.5), which is tight within a factor of O~(√n). The proof, which in addition gives insight into the actual evolution of the contours, requires the introduction of several novel analytical techniques that we conjecture will have other applications.