The Functional Renormalization Group and O(4) scaling

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.

14 pages, 11 figures

References in corpus (10)

• Exact evolution equation for the effective potential
• The QCD Equation of State with almost Physical Quark Masses
• The Phase Diagram of the Quark-Meson Model
• Susceptibilities near the QCD (tri)critical point
• Density fluctuations in the presence of spinodal instabilities
• Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature
• Correlation lengths and scaling functions in the three-dimensional O(4) model
• The 3-D O(4) universality class and the phase transition in two-flavor QCD
• Scaling functions for the O(4)-model in d=3 dimensions
• The Quark-Meson Model and the Phase Diagram of Two-Flavour QCD

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