Abstract
Monte Carlo (MC) simulations and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the ferromagnetic 4-state Potts model on the square lattice are analyzed in a vicinity of the critical point in order to estimate universal combinations of critical amplitudes. The quality of the fits is improved using predictions of the renormalization group (RG) approach and of conformal invariance, and restricting the data within an appropriate temperature window. The RG predictions on the cancelation of the logarithmic corrections in the universal amplitude ratios are tested. A direct calculation of the effective ratio of the energy amplitudes using duality relations explicitly demonstrates this cancelation of logarithms, thus supporting the predictions of RG. We emphasize the role of corrections and of background terms on the determination of the amplitudes. The ratios of the critical amplitudes of the susceptibilities obtained in our analysis differ significantly from those predicted theoretically and supported by earlier SE and MC analysis. This disagreement might signal that the two-kink approximation used in the analytical estimates is not sufficient to describe with fair accuracy the amplitudes of the 4-state model.
Highlights
In a first paper [1], we studied the universal combinations of critical amplitudes of the 3-state Potts model
Analyzing the renormalization group equations, we have shown in an Appendix that, in the absence of any regular background term, the logarithmic corrections cancel in the effective ratio functions
This can be done either directly from the values of the amplitudes listed in the various tables of this paper, or by extrapolating the effective ratios to τ = 0
Summary
In a first paper [1] (hereafter denoted as I), we studied the universal combinations of critical amplitudes of the 3-state Potts model. Analytical estimates of critical amplitude ratios for the q-state Potts models with q = 1, 2, 3, and 4 were recently obtained by Delfino and Cardy [13]. More recently Delfino and Grinza report compatible values in the case of the Ashkin-Teller model, using the same technique at the same level of approximation [19] Another contribution to the study of the amplitude ratios in the 2D 4-state Potts model was reported by Caselle, et al [4]. Obtaining an accurate (say, within a few per cent) and generally accepted approximation of the critical amplitude combinations for the four-state Potts model still remains an open issue both theoretically and numerically
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