Logarithmic corrections and universal amplitude ratios in the 4-state Potts model

Abstract

Monte Carlo and series expansion data for the energy, specific heat, magnetisation and susceptibility of the 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed. Estimates of universal ratios A+/A−, Γ+/ΓL, ΓT /ΓL and R + c are given.

A study of logarithmic corrections and universal amplitude ratios in the two-dimensional 4-state Potts model

“…By the way, in the case of the magnetization the coefficient b is found to be almost zero and we did not include it in eq. ( 14) [21]. Note that these estimates follow from a coherent analysis of both MC data and SE extrapolations.…”

The two-dimensional 4-state Potts model in a magnetic field

“…[1] for details and Refs. [12,14,13,15,16,17,18] for different levels of approximation). Keeping only the leading logarithmic behavior for the present context, expression (34) simply yields What appears extremely useful in these expressions is that when defining appropriate effective ratios, the dependence on the quantity ζ cancels, due to the scaling relations among the critical exponents.…”

“…We now want to explore the values of the 'hat exponents' and the link to universal combinations of critical amplitudes. The particular form taken by the function ζ follows from the solution of equation ( 25), combined to equation (33) iterated at the convenient level of approximation (see appendix of [1] for details and [12][13][14][15][16][17][18] for different levels of approximation). Keeping only the leading logarithmic behavior for the present context, expression (34) simply yields…”

The two-dimensional 4-state Potts model in a magnetic field

“…[1] for details and Refs. [12,14,13,15,16,17,18] for different levels of approximation). Keeping only the leading logarithmic behavior for the present context, expression (34) simply yields…”