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

TL;DR

This paper solves the non-linear renormalization group equations for the 2D 4-state Potts model in a magnetic field, revealing singular behaviors and confirming relations among logarithmic exponents, with implications for universal amplitude ratios.

Contribution

It provides an exact solution to the RG equations for the model, clarifying the nature of singularities and confirming theoretical predictions about logarithmic exponents.

Findings

Exact cancellation of logarithmic corrections in amplitude ratios

Verification of relations among logarithmic exponents

Detailed characterization of singular behaviors at criticality

Abstract

We present a solution of the non-linear renormalization group equations leading to the dominant and subdominant singular behaviours of physical quantities (free energy density, correlation length, internal energy, specific heat, magnetization, susceptibility and magnetocaloric coefficient) at the critical temperature in a non- vanishing magnetic field. The solutions i) lead to exact cancellation of logarithmic corrections in universal amplitude ratios and ii) prove recently proposed relations among logarithmic exponents.