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.

Changes in this version: the explicit formula for n-point spin correlations is proved in full generality. The appendix is rewritten completely and contains this new proof, the introduction is changed accordingly, the presentation in Sections 2.5 and 2.7(2.8) is rearranged slightly. 42 pages, 2 figures

References in corpus (3)

• Exact bosonization of the Ising model
• Dimers and analytic torsion I
• Ising Model: Local Spin Correlations and Conformal Invariance

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• Random loops and conformal field theory
• Ising Model Observables and Non-Backtracking Walks
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus
• Integrability as a consequence of discrete holomorphicity: loop models
• Holomorphic Spinor Observables in the Critical Ising Model
• Conformal Field Theories as Scaling Limit of Anyonic Chains