Antiferromagnetic Potts model on the Erdos-Renyi random graph
Probability
2015-10-07 v4 Disordered Systems and Neural Networks
Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We study the antiferromagnetic Potts model on the Poissonian Erd\"os-R\'enyi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades)and from a positive entropy argument.
Keywords
Cite
@article{arxiv.1106.4714,
title = {Antiferromagnetic Potts model on the Erdos-Renyi random graph},
author = {Pierluigi Contucci and Sander Dommers and Cristian Giardina' and Shannon Starr},
journal= {arXiv preprint arXiv:1106.4714},
year = {2015}
}
Comments
36 pages, revisions to improve result