Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus

TL;DR

This paper calculates universal amplitude ratios for the 2D critical Ising model on a torus using conformal field theory and confirms predictions with high-precision Monte Carlo simulations.

Contribution

It provides the first exact calculations of several universal amplitude ratios and renormalized coupling constants for the 2D Ising model at criticality on a torus.

Findings

Universal amplitude ratios are computed analytically.

Monte Carlo simulations confirm theoretical predictions.

First determination of renormalized 2n-point coupling constants.

Abstract

Using results from conformal field theory, we compute several universal amplitude ratios for the two-dimensional Ising model at criticality on a symmetric torus. These include the correlation-length ratio x^\star = \lim_{L\to\infty} \xi(L)/L and the first four magnetization moment ratios V_{2n} = <{\cal M}^{2n}>/<{\cal M}^2>^n. As a corollary we get the first four renormalized 2n-point coupling constants for the massless theory on a symmetric torus, G_{2n}^*. We confirm these predictions by a high-precision Monte Carlo simulation.