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.
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
Full Article