Scaling violation and the magnetic equation of state in chiral models

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 $N\to \infty$ 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.

14 pages, 8 figures. Extended discussion of the results, slightly changed parameters in calculation for transparency. Additional correction of minor errors and change of format

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Cited by in corpus (4)

• Universal location of the Yang-Lee edge singularity in O(N) theories
• Universality driven analytic structure of the QCD crossover: radius of convergence in the baryon chemical potential
• Fourier coefficients of the net-baryon number density and chiral criticality
• Lee-Yang and Langer edge singularities from analytic continuation of scaling functions