{"title":"Exact solutions for a mean-field Abelian sandpile","authors":"S. A. Janowsky, C. Laberge","doi":"10.1088/0305-4470/26/19/001","DOIUrl":null,"url":null,"abstract":"We introduce a model for a sandpile, with N sites, critical height N and each site connected to every other site. It is thus a mean-field model in the spin-glass sense. We find an exact solution for the steady state probability distribution of avalanche sizes, and discuss its asymptotics for large N.","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Adaptation and Self-Organizing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/26/19/001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 22
Abstract
We introduce a model for a sandpile, with N sites, critical height N and each site connected to every other site. It is thus a mean-field model in the spin-glass sense. We find an exact solution for the steady state probability distribution of avalanche sizes, and discuss its asymptotics for large N.
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