{"title":"Ising模型的几何分析，第三部分","authors":"Michael Aizenman","doi":"10.1007/s11040-025-09528-w","DOIUrl":null,"url":null,"abstract":"<div><p>The random current representation of the Ising model, along with a related path expansion, has been a source of insight on the stochastic geometric underpinning of the ferromagnetic model’s phase structure and critical behavior in different dimensions. This representation is extended here to systems with a mild amount of frustration, such as generated by disorder operators and external field of mixed signs. Examples of the utility of such stochastic geometric representations are presented in the context of the deconfinement transition of the <span>\\(\\mathbb {Z}_2\\)</span> lattice gauge model – particularly in three dimensions– and in streamlined proofs of correlation inequalities with wide-ranging applications.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 4","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Geometric Analysis of Ising Models, Part III\",\"authors\":\"Michael Aizenman\",\"doi\":\"10.1007/s11040-025-09528-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The random current representation of the Ising model, along with a related path expansion, has been a source of insight on the stochastic geometric underpinning of the ferromagnetic model’s phase structure and critical behavior in different dimensions. This representation is extended here to systems with a mild amount of frustration, such as generated by disorder operators and external field of mixed signs. Examples of the utility of such stochastic geometric representations are presented in the context of the deconfinement transition of the <span>\\\\(\\\\mathbb {Z}_2\\\\)</span> lattice gauge model – particularly in three dimensions– and in streamlined proofs of correlation inequalities with wide-ranging applications.</p></div>\",\"PeriodicalId\":694,\"journal\":{\"name\":\"Mathematical Physics, Analysis and Geometry\",\"volume\":\"28 4\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2025-09-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Physics, Analysis and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11040-025-09528-w\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-025-09528-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The random current representation of the Ising model, along with a related path expansion, has been a source of insight on the stochastic geometric underpinning of the ferromagnetic model’s phase structure and critical behavior in different dimensions. This representation is extended here to systems with a mild amount of frustration, such as generated by disorder operators and external field of mixed signs. Examples of the utility of such stochastic geometric representations are presented in the context of the deconfinement transition of the \(\mathbb {Z}_2\) lattice gauge model – particularly in three dimensions– and in streamlined proofs of correlation inequalities with wide-ranging applications.
期刊介绍：
MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas.
The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process.
The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed.
The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
