The Functional Renormalization Group and O(4) scaling

TL;DR

This paper uses the Functional Renormalization Group to analyze the critical behavior of the O(4) symmetric chiral quark-meson model, computing scaling properties and critical exponents near the phase transition.

Contribution

It provides a detailed FRG-based analysis of the O(4) scaling behavior in the chiral quark-meson model, including finite temperature and density effects, and compares results with lattice studies.

Findings

Critical exponents consistent with lattice Monte-Carlo results

Scaling behavior of order parameter and susceptibilities near the phase transition

Validation of the Widom-Griffiths form of the magnetic equation of state

Abstract

The critical behavior of the chiral quark-meson model is studied within the Functional Renormalization Group (FRG). We derive the flow equation for the scale dependent thermodynamic potential at finite temperature and density in the presence of a symmetry-breaking external field. Within this scheme, the critical scaling behavior of the order parameter, its transverse and longitudinal susceptibilities as well as the correlation lengths near the chiral phase transition are computed. We focus on the scaling properties of these observables at non-vanishing external field when approaching the critical point from the symmetric as well as from the broken phase. We confront our numerical results with the Widom-Griffiths form of the magnetic equation of state, obtained by a systematic epsilon-expansion of the scaling function. Our results for the critical exponents are consistent with those recently computed within Lattice Monte-Carlo studies of the O(4) spin system.