Critical Ising correlations on a torus

TL;DR

This paper proves the convergence of multi-point spin correlations in the critical Ising model on a torus, providing explicit formulas for their scaling limits in terms of theta functions, confirming physics predictions.

Contribution

It establishes the convergence of correlations in the critical Ising model on a torus and derives explicit scaling limit formulas using theta functions.

Findings

Convergence of multi-point spin correlations proved.

Explicit formulas for scaling limits in terms of theta functions.

Verification of physics literature predictions.

Abstract

We prove convergence of multi-point spin correlations in the critical Ising model on a torus. Via Pfaffian identities, this also implies convergence of other correlations, including correlations of spins with fermionic and energy observables. We obtain explicit formulae for the scaling limits in terms of theta functions, verifying the predictions in the physics literature.