Communications in Mathematical Physics

, Volume 81, Issue 4, pp 527–602 | Cite as

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

  • Jürg Fröhlich
  • Thomas Spencer


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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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Jürg Fröhlich
    • 1
  • Thomas Spencer
    • 2
  1. 1.Institut des Hautes Études ScintifiquesBures-sur-YvetteFrance
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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