{"title":"Exact S-Matrices","authors":"G. Mussardo","doi":"10.1093/oso/9780198788102.003.0018","DOIUrl":"https://doi.org/10.1093/oso/9780198788102.003.0018","url":null,"abstract":"The Ising model in a magnetic field is one of the most beautiful examples of an integrable model. This chapter presents its exact S-matrix and the exact spectrum of its excitations, which consist of eight particles of different masses. Similarly, it discusses the exact scattering theory behind the thermal deformation of the tricritical Ising model and the unusual features of the exact S-matrix of the non-unitary Yang–Lee model. Other examples are provided by O(n) invariant models, including the important Sine–Gordon model. It also discusses multiple poles, magnetic deformation, the E\u0000 8 Toda theory, bootstrap fusion rules, non-relativistic limits and quantum group symmetry of the Sine–Gordon model.","PeriodicalId":172128,"journal":{"name":"Statistical Field Theory","volume":"31 13","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113976070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum Field Theory","authors":"G. Mussardo","doi":"10.1093/oso/9780198788102.003.0007","DOIUrl":"https://doi.org/10.1093/oso/9780198788102.003.0007","url":null,"abstract":"Chapter 7 covers the main reasons for adopting the methods of quantum field theory (QFT) to study the critical phenomena. It presents both the canonical quantization and the path integral formulation of the field theories as well as the analysis of the perturbation theory. The chapter also covers transfer matrix formalism and the Euclidean aspects of QFT, the field theory of the Ising model, Feynman diagrams, correlation functions in coordinate space, the Minkowski space and the Legendre transformation and vertex functions. Everything in this chapter will be needed sooner or later, since it highlights most of the relevant aspects of quantum field theory.","PeriodicalId":172128,"journal":{"name":"Statistical Field Theory","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114743068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L. Bonora, G. Mussardo, A. Schwimmer, L. Girardello, M. Martellini
{"title":"Integrable Quantum Field Theories","authors":"L. Bonora, G. Mussardo, A. Schwimmer, L. Girardello, M. Martellini","doi":"10.1007/978-1-4899-1516-0","DOIUrl":"https://doi.org/10.1007/978-1-4899-1516-0","url":null,"abstract":"","PeriodicalId":172128,"journal":{"name":"Statistical Field Theory","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123407118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Approximate Solutions","authors":"G. Mussardo","doi":"10.1093/oso/9780198788102.003.0003","DOIUrl":"https://doi.org/10.1093/oso/9780198788102.003.0003","url":null,"abstract":"Chapter 3 discusses the approximation schemes used to approach lattice statistical models that are not exactly solvable. In addition to the mean field approximation, it also considers the Bethe–Peierls approach to the Ising model. Moreover, there is a thorough discussion of the Gaussian model and its spherical version, both of which are two important systems with several points of interest. A chapter appendix provides a detailed analysis of the random walk on different lattices: apart from the importance of the subject on its own, it explains how the random walk is responsible for the critical properties of the spherical model.","PeriodicalId":172128,"journal":{"name":"Statistical Field Theory","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132310637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Conformal Field Theory","authors":"G. Mussardo","doi":"10.1093/oso/9780198788102.003.0010","DOIUrl":"https://doi.org/10.1093/oso/9780198788102.003.0010","url":null,"abstract":"Chapter 10 introduces the notion of conformal transformations and the important topic of the massless quantum field theories associated to the critical points of the statistical models. The chapter establishes the important conceptual result that the classification of all possible critical phenomena in two dimensions consists of finding out all possible irreducible representations of the Virasoro algebra. It covers the algebra of local fields, conformal invariance, Polyakov's theorem, quasi-primary fields, Ward identity, primary fields, the Schwartz derivative, the representation theory, radial quantization, the Hilbert space of conformal states, the use of the Cauchy formula, orthogonality of conformal families and structure constants of descendant fields.","PeriodicalId":172128,"journal":{"name":"Statistical Field Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117064310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum Field Theory","authors":"J. Narlikar, T. Padmanabhan","doi":"10.1007/978-94-009-4508-1_4","DOIUrl":"https://doi.org/10.1007/978-94-009-4508-1_4","url":null,"abstract":"","PeriodicalId":172128,"journal":{"name":"Statistical Field Theory","volume":" 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141220677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"One-dimensional Systems","authors":"G. Mussardo","doi":"10.1093/oso/9780198788102.003.0002","DOIUrl":"https://doi.org/10.1093/oso/9780198788102.003.0002","url":null,"abstract":"Chapter 2 discusses one-dimensional statistical models, for example, the Ising model and its generalizations (Potts model, systems with O(n) or Zn-symmetry, etc.). It discusses several methods of solution and covers the recursive method, the transfer matrix approach, and series expansion techniques. General properties of these methods, which are valid on higher-dimensional lattices, are also covered. The contents of this chapter are quite simple and pedagogical but extremely useful for understanding the following sections of the book. One of the appendices at the end of the chapter is devoted to a famous problem of topology, i.e. the four-colour problem, and its relation with the two-dimensional Potts model.","PeriodicalId":172128,"journal":{"name":"Statistical Field Theory","volume":"2015 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121602072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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