Conformal Invariance of Spin Correlations in the Planar Ising Model

TL;DR

This paper proves the conformal invariance of spin correlations in the critical planar Ising model, confirming longstanding conjectures through rigorous mathematical methods.

Contribution

It establishes the existence and conformal invariance of scaling limits of spin correlations in arbitrary simply connected domains, advancing theoretical understanding.

Findings

Conformal invariance of spin correlations is rigorously proven.

Scaling limits exist for magnetization and multi-point correlations.

Results confirm several conjectures from physics and mathematics literature.

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.