{"title":"Kac–Ward Solution of the 2D Classical and 1D Quantum Ising Models","authors":"Georgios Athanasopoulos, Daniel Ueltschi","doi":"10.1007/s00023-024-01479-2","DOIUrl":null,"url":null,"abstract":"<p>We give a rigorous derivation of the free energy of (i) the classical Ising model on the triangular lattice with translation-invariant coupling constants and (ii) the one-dimensional quantum Ising model. We use the method of Kac and Ward. The novel aspect is that the coupling constants may have negative signs. We describe the logarithmic singularity of the specific heat of the classical model and the validity of the Cimasoni–Duminil-Copin–Li formula for the critical temperature. We also discuss the quantum phase transition of the quantum model.\n</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://doi.org/10.1007/s00023-024-01479-2","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We give a rigorous derivation of the free energy of (i) the classical Ising model on the triangular lattice with translation-invariant coupling constants and (ii) the one-dimensional quantum Ising model. We use the method of Kac and Ward. The novel aspect is that the coupling constants may have negative signs. We describe the logarithmic singularity of the specific heat of the classical model and the validity of the Cimasoni–Duminil-Copin–Li formula for the critical temperature. We also discuss the quantum phase transition of the quantum model.
期刊介绍：
The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society.
The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.
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