Conformal Invariance of Spin Correlations in the Planar Ising Model
Mathematical Physics
2014-07-17 v3 Complex Variables
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1202.2838,
title = {Conformal Invariance of Spin Correlations in the Planar Ising Model},
author = {Dmitry Chelkak and Clément Hongler and Konstantin Izyurov},
journal= {arXiv preprint arXiv:1202.2838},
year = {2014}
}
Comments
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