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Holomorphic Spinor Observables in the Critical Ising Model

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Abstract

We introduce a new version of discrete holomorphic observables for the critical planar Ising model. These observables are holomorphic spinors defined on double covers of the original multiply connected domain. We compute their scaling limits, and show their relation to the ratios of spin correlations, thus providing a rigorous proof to a number of formulae for those ratios predicted by CFT arguments.

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Author notes

  1. Konstantin Izyurov

    Present address: Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, 00014, Helsinki, Finland

Authors and Affiliations

  1. St.Petersburg Department of Steklov Mathematical Institute (PDMI RAS), Fontanka 27, 191023, St.Petersburg, Russia

    Dmitry Chelkak

  2. Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, Case postale 64, 1211, Genève 4, Suisse

    Konstantin Izyurov

  3. Chebyshev Laboratory, Department of Mathematics and Mechanics, Saint-Petersburg State University, 14th Line, 29b, 199178, Saint-Petersburg, Russia

    Dmitry Chelkak & Konstantin Izyurov

Authors
  1. Dmitry Chelkak
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  2. Konstantin Izyurov
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Correspondence to Dmitry Chelkak.

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Communicated by M. Aizenman

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Chelkak, D., Izyurov, K. Holomorphic Spinor Observables in the Critical Ising Model. Commun. Math. Phys. 322, 303–332 (2013). https://doi.org/10.1007/s00220-013-1763-5

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  • DOI: https://doi.org/10.1007/s00220-013-1763-5

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