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

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.

arXiv comment32 pages, 9 figures, 11 tables

References in corpus (11)

• Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
• Universal amplitude ratios in the two-dimensional $q$-state Potts model and percolation from quantum field theory
• Universal ratios along a line of critical points. The Ashkin--Teller model
• Series studies of the Potts model. II: Bulk series for the square lattice
• Susceptibility amplitude ratios in the two-dimensional Potts model and percolation
• On the quality of random number generators with taps
• Critical amplitude ratios of the Baxter-Wu model
• Universal amplitude ratios in the 2D four state Potts model
• High-precision determination of universal amplitude ratios for the q=3 Potts model in 2d
• Susceptibility amplitude ratio in the two-dimensional three-state Potts model
• A study of logarithmic corrections and universal amplitude ratios in the two-dimensional 4-state Potts model

Cited by in corpus (8)

• Normal form for renormalization groups
• Critical amplitude ratios of the Baxter-Wu model
• Universal amplitude ratios of two-dimensional percolation from field theory
• Critical phenomena on scale-free networks: logarithmic corrections and scaling functions
• The two-dimensional 4-state Potts model in a magnetic field
• Revisiting (logarithmic) scaling relations using renormalization group
• Interfacial adsorption in two-dimensional pure and random-bond Potts models
• Machine Learning Domain Adaptation in Spin Models with Continuous Phase Transitions