Universal critical dynamics near the chiral phase transition and the QCD critical point

¹ Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
² Institut für Theoretische Physik, Justus-Liebig-Universität, 35392 Giessen, Germany
³ Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany
⁴ Helmholtz Research Academy Hesse for FAIR (HFHF), Campus Giessen, 35392 Giessen, Germany

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Published online: 17 April 2026

Abstract

We use a novel real-time formulation of the functional renormalization group (FRG) for dynamical systems with reversible mode couplings to study Model G and H, which are the conjectured dynamic universality classes of the two-flavor chiral phase transition and the QCD critical point, respectively. We compute the dynamic critical exponent in both models in spatial dimensions 2 < d < 4. We discuss qualitative commonalities and differences in the non-perturbative RG flow, such as weak scaling relations which hold in either case versus the characteristic strong scaling of Model G which is absent in Model H. For Model G, we also extract a novel dynamic scaling function that describes the universal momentum and temperature dependence of the diffusion coefficient of iso-(axial-)vector charges in the symmetric phase.