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AC*-algebra of the two-dimensional Ising model

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Abstract

We consider the two-dimensional Ising model and show how correlation functions are determined by a state of aC*-Clifford algebra. We describe how the phase transition manifests itself in terms of a jump in the index of a Fredholm operator. A connection with the Pfaffian approach is made through the theory of unitary dilations of contraction semigroups.

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Authors and Affiliations

  1. Institute for Advanced Studies, Dublin 4, Ireland

    J. T. Lewis

  2. University of Leuven, Leuven, Belgium

    P. N. M. Sisson

Authors
  1. J. T. Lewis
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  2. P. N. M. Sisson
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Communicated by G. Gallavotti

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Lewis, J.T., Sisson, P.N.M. AC*-algebra of the two-dimensional Ising model. Commun.Math. Phys. 44, 279–292 (1975). https://doi.org/10.1007/BF01609831

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  • DOI: https://doi.org/10.1007/BF01609831

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