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

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⋆ = limL→∞ ξ(L)/L and the first four magnetization moment ratios V2n = 〈M2n〉/〈M2〉n. As a corollary we get the renormalized four-point coupling constant for the massless theory on a symmetric torus, G∗ = (3 − V4)/x. We confirm these predictions by a high-precision Monte Carlo simulation. The finite-size-scaling behavior of our data is consistent with the prediction that the leading correction to finite-size scaling in the susceptibility is the regular background. As a by-product, we also analyze the dynamic critical behavior of the Swendsen-Wang algorithm for this model: we find that the ratio τint,E/CH tends to infinity either as a logarithm A logL+B or as a power-law ALp with a small power p ≈ 0.06.