The relation between amplitudes and critical exponents in finite-size scaling

Abstract

The relation between critical exponents and the amplitude of the correlation length divergence at the critical point of two-dimensional systems as a function of finite size is investigated and generalised in two ways. Correlations more general than those of order-order type are included. A form appropriate for anisotropic systems is proposed. The authors present (a) exact results for the Ising and Gaussian models and (b) numerical results for the symmetric eight-vertex (Baxter), continuous q-state Potts, and continuous N-component cubic models.