On the Potts antiferromagnet on random graphs
type: Item
instance of: scholarly article
title: On the Potts antiferromagnet on random graphs
zbMATH Open document ID: 1351.05203
author: Amin Coja-Oghlan
author: Nor Jaafari
published in: The Electronic Journal of Combinatorics
publication date: 2016-12-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/1603.00081
full work available at URL: v23i4p3
review text: Summary: Extending a prior result of \textit{P. Contucci} et al. [Commun. Math. Phys. 323, No. 2, 517--554 (2013; Zbl 1285.82007)], we determine the free energy of the Potts antiferromagnet on the Erdős-Rényi random graph at all temperatures for average degrees \(d\leq (2k-1)\ln k - 2 - k^{-1/2}\). In particular, we show that for this regime of \(d\) there does not occur a phase transition.
Mathematics Subject Classification ID: 05C80
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 82B26
Mathematics Subject Classification ID: 82B27
zbMATH DE Number: 6661355
zbMATH Keywords: Potts model
zbMATH Keywords: random graphs
MaRDI profile type: Publication
arXiv ID: 1603.00081
cites work: Q4705349
cites work: The two possible values of the chromatic number of a random graph
cites work: Hypergraph coloring up to condensation
cites work: The condensation phase transition in the regular $k$-SAT model
cites work: The condensation phase transition in random graph coloring
cites work: A positive temperature phase transition in random hypergraph 2-coloring
cites work: Q3056951
cites work: Decay of correlations for the hardcore model on the \(d\)-regular random graph
cites work: Upper-bounding the \(k\)-colorability threshold by counting covers
cites work: On the chromatic number of random regular graphs
cites work: The Chromatic Number of Random Graphs for Most Average Degrees
cites work: Antiferromagnetic Potts model on the Erdős-Rényi random graph
cites work: The replica symmetric solution for Potts models on \(d\)-regular graphs
cites work: On the chromatic number of a random hypergraph
cites work: MCMC sampling colourings and independent sets of G(n, d/n) near uniqueness threshold
cites work: Switching Colouring of G(n,d/n) for Sampling up to Gibbs Uniqueness Threshold
cites work: Q3286850
cites work: Q4519896
cites work: On the chromatic number of random \(d\)-regular graphs
cites work: Gibbs states and the set of solutions of random constraint satisfaction problems
cites work: Information, Physics, and Computation
cites work: Reconstruction on trees and spin glass transition
cites work: The freezing threshold for k-colourings of a random graph
description: scientific article