English

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

R2 v1 2026-06-21T18:26:33.178Z