Manifest Modular Invariance in the Near-Critical Ising Model

TL;DR

This paper demonstrates how modular invariance can be explicitly shown in the free energies and scale-dependent central charges of the near-critical Ising model, revealing new insights into finite-size effects and automorphic symmetries.

Contribution

It introduces a novel mathematical framework that makes modular invariance manifest in the analysis of near-critical models, extending beyond the Ising model to automorphic symmetries.

Findings

Explicit representation of free energies with manifest modular invariance

Application to finite-size effects in the near-critical Ising model

Extension of methods to automorphic symmetries

Abstract

Using recent results in mathematics, I point out that free energies and scale-dependent central charges away from criticality can be represented in compact form where modular invariance is manifest. The main example is the near-critical Ising model on a thermal torus, but the methods are not restricted to modular symmetry, and apply to automorphic symmetries more generally. One application is finite-size effects.