The scale dependence of an effective average action for mesons and quarks is described by a nonperturbative flow equation. The running couplings lead to spontaneous chiral symmetry breaking. We argue that for strong Yukawa coupling between quarks and mesons the low momentum physics is essentially determined by infrared fixed points. This allows us to establish relations between various parameters related to the meson potential. The results for f π and ψψ are not very sensitive to the poorly known details of the quark-meson effective action at scales where the mesonic bound states form. For realistic constituent quark masses we find f π around 100 MeV.

We employ nonperturbative flow equations to compute the equation of state for two flavor QCD within an effective quark meson model. This yields the temperature and quark mass dependence of quantities like the chiral condensate or the pion mass. 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.

We investigate the QCD chiral phase transition at high baryon number density within the linear quark meson model for two flavors. The method we employ is based on an exact renormalization group equation for the free energy. Truncated nonperturbative flow equations are derived at nonzero chemical potential and temperature. Whereas the renormalization group flow leads to spontaneous chiral symmetry breaking in vacuum, we find a chiral symmetry restoring first order transition at high density. Combined with previous investigations at nonzero temperature, the result implies the presence of a tricritical point with long-range correlations in the phase diagram. †

We present an analytical description of the phase transitions from a nucleon gas to nuclear matter and from nuclear matter to quark matter within the same model. The equation of state for quark and nuclear matter is encoded in the effective potential of a linear sigma model. We exploit an exact differential equation for its dependence upon the chemical potential $\mu$ associated to conserved baryon number. An approximate solution for vanishing temperature is used to discuss possible phase transitions as the baryon density increases. For a nucleon gas and nuclear matter we find a substantial density enhancement as compared to quark models which neglect the confinement to baryons. The results point out that the latter models are not suitable to discuss the phase diagram at low temperature.Comment: 27 pages, Int.J.Mod.Phys.A versio

A wide class of models involve the fine-tuning of significant hierarchies between a strong-coupling "compositeness" scale, and a low energy dynamical symmetry breaking scale. We examine the issue of whether such hierarchies are generally endangered by Coleman-Weinberg instabilities. A careful study using perturbative two-loop renormalization group methods finds that consistent large hierarchies are not generally disallowed.