{"title":"具有竞争性相互作用的一维伊辛模型产生的随机过程","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":" 64","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\" 64\",\"pages\":\"\"},\"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}","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}
Stochastic process generated by 1-D Ising model with competing interactions
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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