Eur. Phys. J. C (2010) 67: 425-438
https://doi.org/10.1140/epjc/s10052-010-1310-x

Regular Article - Theoretical Physics

The functional renormalization group and O(4) scaling

¹ Gesellschaft für Schwerionenforschung, GSI, 64291, Darmstadt, Germany
² Institute of Theoretical Physics, University of Wroclaw, 50204, Wrocław, Poland
³ Institut für Kernphysik, Technical University Darmstadt, 64289, Darmstadt, Germany

^* e-mail: redlich@ift.uni.wroc.pl

Received: 13 August 2009
Revised: 16 February 2010
Published online: 21 April 2010

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. We perform a set of approximations to formulate and solve the FRG flow equation in the presence of fermionic degrees of freedom and test their influence on the O(4) critical properties expected in the quark-meson model. 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 for vanishing baryon density. 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 ε expansion of the scaling function.