Numerical revision of the universal amplitude ratios for the two-dimensional 4-state Potts model

TL;DR

This paper refines the numerical estimates of universal amplitude ratios in the 2D 4-state Potts model using Monte Carlo and series expansion data, testing renormalization group predictions and highlighting discrepancies with theoretical estimates.

Contribution

It provides improved numerical estimates of universal amplitude ratios and tests RG predictions on logarithmic correction cancelation in the 4-state Potts model.

Findings

Confirmation of logarithmic correction cancelation in amplitude ratios

Discrepancies between numerical results and theoretical predictions for susceptibility ratios

Highlighting the impact of background correction terms on amplitude determination

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 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.