Scaling violation and the magnetic equation of state in chiral models

TL;DR

This paper investigates the scaling behavior of the order parameter at the chiral phase transition in strongly interacting matter using effective models, analyzing universal and nonuniversal structures near the critical point.

Contribution

It compares critical properties of quark-meson and PQM models with the $O(N)$ linear sigma model, providing analytical scaling functions and studying gluonic effects.

Findings

Analytical scaling functions derived for the models.

Identification of the scaling window and corrections.

Effects of gluonic background on nonuniversal parameters.

Abstract

The scaling behavior of the order parameter at the chiral phase transition, the so-called magnetic equation of state, of strongly interacting matter is studied within effective models. We explore universal and nonuniversal structures near the critical point. These include the scaling functions, the leading corrections to scaling, and the corresponding size of the scaling window as well as their dependence on an external symmetry breaking field. We consider two models in the mean-field approximation, the quark-meson and the Polyakov loop extended quark-meson (PQM) models, and compare their critical properties with a purely bosonic theory, the $O(N)$ linear sigma model in the $N\rightarrow \infty$ limit. In these models the order parameter scaling function is found analytically using the high temperature expansion of the thermodynamic potential. The effects of a gluonic background on the nonuniversal scaling parameters are studied within the PQM model.