Free Energy, Gibbs Measures, and Glauber Dynamics for Nearest-neighbor Interactions on Trees
Probability
2020-11-03 v1
Abstract
We extend results of R. Holley beyond the integer lattice to a large class of groups which includes free groups. In particular we show that a shift-invariant measure is Gibbs if and only if it is Glauber-invariant. Moreover, any shift-invariant measure converges weakly to the set of Gibbs measures when evolved under Glauber dynamics. These results are proven using a new notion of free energy density relative to a sofic approximation by homomorphisms. Any measure which minimizes free energy density is Gibbs.
Keywords
Cite
@article{arxiv.2011.00653,
title = {Free Energy, Gibbs Measures, and Glauber Dynamics for Nearest-neighbor Interactions on Trees},
author = {Christopher Shriver},
journal= {arXiv preprint arXiv:2011.00653},
year = {2020}
}