Bernd-Jochen Schaefer

The phase diagram of the quark–meson model

Abstract Within the proper-time renormalization group approach, the chiral phase diagram of a two-flavor quark–meson model is studied. In the chiral limit, the location of the tricritical point which is linked to a Gaussian fixed point, is determined. For quark chemical potentials smaller than the tricritical one the second-order phase transition belongs to the O ( 4 ) universality class. For temperatures below the tricritical one we find initially a weak first-order phase transition which is commonly seen in model studies and also in recent lattice simulations. In addition, below temperatures of T ≲ 17 MeV we find two phase transitions. The chiral restoration transition is initially also of first-order but turns into a second-order transition again. This leads to the possibility that there may be a “second tricritical” point in the QCD phase diagram in the chiral limit.

Susceptibilities near the QCD (tri)critical point

Based on the proper-time renormalization group approach, the scalar and the quark number susceptibilities in the vicinity of possible critical end points of the hadronic phase diagram are investigated in the two-flavor quark-meson model. After discussing the quark-mass dependence of the location of such points, the critical behavior of the in-medium meson masses and quark number density are calculated. The universality classes of the end points are determined by calculating the critical exponents of the susceptibilities. In order to numerically estimate the influence of fluctuations we compare all quantities with results from a mean-field approximation. It is concluded that the region in the phase diagram where the susceptibilities are enhanced is more compressed around the critical end point if fluctuations are included.

The equation of state of quarks and mesons in a renormalization group flow picture

Abstract Non-perturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavours are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second-order phase transition at Tc≈150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.Nonperturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavors are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second order phase transition at T_c approx 150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.

RENORMALIZATION GROUP FLOW EQUATIONS AND THE PHASE TRANSITION IN O(N)-MODELS

We derive and solve numerically self-consistent flow equations for a general O(N)-symmetric effective potential without any polynomial truncation. The flow equations combined with a sort of a heat-kernel regularization are approximated in next-to-leading order of the derivative expansion. We investigate the method at finite temperature and study the nature of the phase transition in detail. Several beta functions, the Wilson–Fisher fixed point in three dimensions for various N are analyzed and various critical exponents β, ν, δ and η are independently calculated in order to emphasize the reliability of this novel approach.

Convergence of the expansion of the renormalization group flow equation

We compare and discuss the dependence of a polynomial truncation of the effective potential used to solve an exact renormalization group flow equation for a model with a fermionic interaction (linear sigma model) with a grid solution. The sensitivity of the results to the underlying cutoff function is discussed. We explore the validity of the expansion method for second- and first-order phase transitions. (c) 2000 The American Physical Society.

Finite-temperature gluon condensate with renormalization group flow equations

Within a self-consistent proper-time Renormalization Group (RG) approach we investigate an effective QCD trace anomaly realization with dilatons and determine the finite-temperature behavior of the gluon condensate. Fixing the effective model at vanishing temperature to the glueball mass and the bag constant a possible gluonic phase transition is explored in detail. Within the RG framework the full non-truncated dilaton potential analysis is compared with a truncated potential version.

Renormalization group flow equations for the scalar O(N) theory

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.