Conformal Invariance of Spin Correlations in the Planar Ising Model

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 discreteholomorphic spinor observables and probabilistic techniques.

Published in:
Annals of Mathematics, 181, 1087-1138
Year:
2015
ISSN:
0003-486X
Laboratories: