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Phase Transitions in Statistical Mechanics and Quantum Field Theory

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Book cover New Developments in Quantum Field Theory and Statistical Mechanics Cargèse 1976

Part of the book series: Nato Advanced Study Institutes Series ((ASIB,volume 26))

Abstract

These lectures are a survey of some mathematically rigorous results concerning phase transitions and symmetry breaking in statistical mechanics and quantum field theory. This subject has a rather long history: The first results on phase transitions were obtained by R. Peierls in 1936, [Pe]. He showed that the Ising model in two or more dimensions has spontaneous magnetization at low temperatures. His argument was later reformulated in various ways and applied to many model systems. See the references in [Gr]. We shall apply a variant of the Peierls argument [GJS3] to prove that there is a phase transition in the two dimensional, anisotropic (→φ·→φ)2 quantum field model in two dimensions and we explain how, in this model, a phase transition gives rise to soliton sectors. We show that the mass gap on the soliton sector is bounded below by the “surface tension” of this model.

A. P. Sloan Foundation Fellows.

Supported in part by NSF under contract NSF-PHY-7617191

Supported in part by NSF under contract NSF-MCS-75-11864

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Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, N. J., 08540, USA

    J. Fröhlich

  2. Department of Mathematics, Rockefeller University, New York, N. Y., 10021, USA

    T. Spencer

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  1. J. Fröhlich
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  2. T. Spencer
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Editor information

Editors and Affiliations

  1. Laboratory of Theoretical Physics and High Energies, Université Pierre et Marie Curie, Paris, France

    Maurice Lévy  & Pronob Mitter  & 

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© 1977 Plenum Press, New York

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Fröhlich, J., Spencer, T. (1977). Phase Transitions in Statistical Mechanics and Quantum Field Theory. In: Lévy, M., Mitter, P. (eds) New Developments in Quantum Field Theory and Statistical Mechanics Cargèse 1976. Nato Advanced Study Institutes Series, vol 26. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8918-1_4

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  • DOI: https://doi.org/10.1007/978-1-4615-8918-1_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-8920-4

  • Online ISBN: 978-1-4615-8918-1

  • eBook Packages: Springer Book Archive

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