{"title":"Color symmetry breaking in the Potts spin glass","authors":"Jean-Christophe Mourrat","doi":"arxiv-2409.10437","DOIUrl":null,"url":null,"abstract":"The Potts spin glass is an analogue of the Sherrington-Kirkpatrick model in\nwhich each spin can take one of $\\kappa$ possible values, which we interpret as\ncolors. It was suggested in arXiv:2310.06745 that the order parameter for this\nmodel is always invariant with respect to permutations of the colors. We show\nhere that this is false whenever $\\kappa \\ge 58$.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10437","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The Potts spin glass is an analogue of the Sherrington-Kirkpatrick model in
which each spin can take one of $\kappa$ possible values, which we interpret as
colors. It was suggested in arXiv:2310.06745 that the order parameter for this
model is always invariant with respect to permutations of the colors. We show
here that this is false whenever $\kappa \ge 58$.