{"title":"Stochastic process generated by 1-D Ising model with competing interactions","authors":"N.N. Ganikhodjaev","doi":"10.3842/tsp-2702069172-88","DOIUrl":null,"url":null,"abstract":"\nWe consider a stochastic process generated by 1-D Ising model with competing interactions and describe all distributions of this process.\nIt is shown that the set of all limit Gibbs measures, i.e. phase diagram, consist of ferromagnetic, anti-ferromagnetic, paramagnetic and modulated phases.\nAlso it is proven that on the set of ferromagnetic phases one can reach the phase transition. \n","PeriodicalId":38143,"journal":{"name":"Theory of Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Stochastic Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3842/tsp-2702069172-88","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a stochastic process generated by 1-D Ising model with competing interactions and describe all distributions of this process.
It is shown that the set of all limit Gibbs measures, i.e. phase diagram, consist of ferromagnetic, anti-ferromagnetic, paramagnetic and modulated phases.
Also it is proven that on the set of ferromagnetic phases one can reach the phase transition.
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