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 renormalized four-point coupling constant for the massless theory on a symmetric torus, G^* = (3-V_4)/x^{\star 2}. 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 \tau_{int,{\cal E}}/C_H$ tends to infinity either as a logarithm A \log L + B or as a power-law A L^p with a small power p \approx 0.06.Keywords
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