Phase transition for the Ising model on the Critical Lorentzian triangulation
Probability
2008-10-14 v1 Combinatorics
Abstract
Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs measures at low temperature. The proofs are based on the disagreement percolation method and on a variant of Peierls method. The critical temperature is shown to be constant a.s.
Keywords
Cite
@article{arxiv.0810.2182,
title = {Phase transition for the Ising model on the Critical Lorentzian triangulation},
author = {Maxim Krikun and Anatoly Yambartsev},
journal= {arXiv preprint arXiv:0810.2182},
year = {2008}
}