The Quark-Meson Model and the Phase Diagram of Two-Flavour QCD

TL;DR

This paper explores the phase diagram of two-flavour QCD using the quark-meson model and renormalization group techniques, identifying universality classes, critical points, and phase transition behaviors.

Contribution

It provides a detailed analysis of the QCD phase diagram with explicit and spontaneous chiral symmetry breaking, highlighting the universality classes and critical phenomena involved.

Findings

Identification of the tricritical point linked to the Gaussian fixed point.

Universal crossover between Gaussian and O(4) fixed points.

Decoupling of pion fluctuations at the critical endpoint.

Abstract

We study the qualitative features of the QCD phase diagram in the context of the linear quark-meson model with two flavours, using the exact renormalization group. We identify the universality classes of the second-order phase transitions and calculate critical exponents. In the absence of explicit chiral-symmetry breaking through the current quark masses, we discuss in detail the tricritical point and demonstrate that it is linked to the Gaussian fixed point. In its vicinity we study the universal crossover between the Gaussian and O(4) fixed points, and the weak first-order phase transitions. In the presence of explicit chiral-symmetry breaking, we study in detail the critical endpoint of the line of first-order phase transitions. We demonstrate the decoupling of pion fluctuations and identify the Ising universality class as the relevant one for the second-order phase transition.