Flow Equations for Phase Transitions in Statistical Physics and QCD

TL;DR

This paper reviews the effective average action formalism in quantum field theory, applying it to phase transitions in statistical physics and QCD, including chiral symmetry breaking and critical phenomena.

Contribution

It provides a detailed analysis of the renormalization group approach and applies it to QCD and O(N) models, offering new insights into phase transitions and critical behavior.

Findings

Emergence of mesonic states and chiral symmetry breaking in QCD

Universal critical equation of state for 3D O(4) model

Pion correlation length behavior near T_c

Abstract

We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative approximations for its solution are discussed. We describe in detail O(N)-symmetric scalar theories in two and three dimensions. These ideas are also applied to QCD where one observes the consecutive emergence of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We finally present a study of the chiral phase transition in two flavor QCD. A precision estimate of the universal critical equation of state for the three-dimensional O(4) Heisenberg model is presented. We explicitly connect the O(4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near T_c turns out to be smaller than its zero temperature value.