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

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.

Comments: 36 pages (LaTeX with style files included). Paper drastically shortened: discussion of corrections to scaling and SW dynamics deferred to future work. Analysis of higher renormalized coupling constants G_{2n}^* added. New bibliography added. To appear in J. Stat. Phys