Year: 2010
Type: preprint
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 $O~(n^{3.5})$, which is tight within a factor of $O~(sqrt{n})$. (The notation O~ hides factors that are logarithmic in 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.
Source: arXiv (Cornell University)
Authors: Martinelli, Fabio, Sinclair, Alistair
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2952915795