Manifest Modular Invariance in the Near-Critical Ising Model

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.

arXiv comment23 pages, 7 figures

References in corpus (8)

• La fonction Zeta de Riemann prend une infinite de valeurs irrationnelles aux entiers impairs
• Eisenstein series and automorphic representations
• Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus
• Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus
• Towards the One-loop Kahler Metric of Calabi-Yau Orientifolds
• Transition from the ${\mathbb{Z}}_2$ spin liquid to antiferromagnetic order: spectrum on the torus
• $T\overline{T}$-deformed modular forms
• Modular symmetry of massive free fermions