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The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas

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Abstract

We rigorously establish the existence of a Kosterlitz-Thouless transition in the rotator, the Villain, the solid-on-solid, and the ℤ n models, forn large enough, and in the Coulomb lattice gas, in two dimensions. Our proof is based on an inductive expansion of the Coulomb gas in the sine-Gordon representation, extending over all possible distance scales, which expresses that gas as a convex superposition of dilute gases of neutral molecules whose activities are small if β is sufficiently large. Such gases are known not to exhibit screening. Abelian spin systems are related to a Coulomb gas by means of a duality transformation.

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Author notes

  1. Jürg Fröhlich

    Present address: Physics Dept., ETH, Zürich, Switzerland

Authors and Affiliations

  1. Institut des Hautes Études Scintifiques, 35, Route de Chartres, F-91440, Bures-sur-Yvette, France

    Jürg Fröhlich

  2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012, New York, NY, USA

    Thomas Spencer

Authors
  1. Jürg Fröhlich
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  2. Thomas Spencer
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Additional information

Communicated by A. Jaffe

Work supported in part by Grant NSF-DMR 79-04355 and 81-00417

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Fröhlich, J., Spencer, T. The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas. Commun.Math. Phys. 81, 527–602 (1981). https://doi.org/10.1007/BF01208273

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  • DOI: https://doi.org/10.1007/BF01208273

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