Conformal invariance of spin correlations in the planar Ising model

Abstract

We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming from the physical and the mathematical literature. The proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques.

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Authors

Dmitry Chelkak

St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg, Russia, Chebyshev Laboratory, Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

Current address:

ETH Zürich, Institute for Theoretical Studies, Zürich, Switzerland Clément Hongler

Columbia University, New York, NY

Current address:

École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland Konstantin Izyurov

Chebyshev Laboratory, Department of Mathematics and
Mechanics, St. Petersburg State University, St. Petersburg, Russia

Current address:

University of Helsinki, Helsinki, Finland