波茨自旋玻璃中的色彩对称破缺

arXiv - MATH - Probability Pub Date : 2024-09-16 DOI:arxiv-2409.10437

Jean-Christophe Mourrat

{"title":"波茨自旋玻璃中的色彩对称破缺","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":"{\"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}","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

摘要

波茨自旋玻璃是谢林顿-柯克帕特里克（Sherrington-Kirkpatrick）模型的一个类似物，其中每个自旋都可以取$\kappa$可能值中的一个，我们将其解释为颜色。有人在 arXiv:2310.06745 中提出，这个模型的阶次参数在颜色的排列上总是不变的。我们在这里证明，只要 $\kappa \ge 58$，这就是假的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Color symmetry breaking in the Potts spin glass

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 $\kappa \ge 58$.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Probability

自引率

0.00%

发文量