Chiral Symmetry Restoration at Finite Temperature in the Linear Sigma--Model

The temperature behaviour of meson condensates $$and$$ is calculated in the $SU(3)\times SU(3)$-linear sigma model. The couplings of the Lagrangian are fitted to the physical $\pi,K,\eta,\eta'$ masses, the pion decay constant and a $O^+(I=0)$ scalar mass of $m_\sigma=1.5$ GeV. The quartic terms of the mesonic interaction are converted to a quadratic term with the help of a Hubbard-Stratonovich transformation. Effective mass terms are generated this way, which are treated self-consistently to leading order of a $1/N$-expansion. We calculate the light $$ and strange $<\bar s s>$-quark condensates using PCAC relations between the meson masses and condensates. For a cut-off value of 1.5 GeV we find a first-order chiral transition at a critical temperature $T_c\sim 161$ MeV. At this temperature the spontaneously broken subgroup $SU(2)\times SU(2)$ is restored. Entropy density, energy density and pressure are calculated for temperatures up to and slightly above the critical temperature. To our surprise we find some indications for a reduced contribution from strange mesons for $T\geq T_c$.Comment: 17 pages, HD--TVP--93--15. (3 figures - available on request

Radiatively-Induced First-Order Phase Transitions: The Necessity of the Renormalization Group

We advocate a (Wilson) renormalization-group (RG) treatment of finite-temperature first-order phase transitions, in particular those driven by radiative corrections such as occur in the standard model, and other spontaneously-broken gauge theories. We introduce the scale-dependent coarse-grained free energy S_\La[\phi] which we explicitly calculate, using the Wilson RG and a (4-\ep)-expansion, for a scalar toy model that shares many features of the gauged case. As argued by Langer and others, the dynamics of the phase transition are described by S_\La[\phi] with \La of order the bubble wall thickness, and {\it not} by the usual (RG-improved) finite-temperature effective action which is reproduced by S_\La[\phi] for \La\to 0. We argue that for weakly first-order transitions (such as that in the standard model) the (4-\ep)-expansion is necessary to control an inevitable growth of the effective scale-dependent coupling towards the strong-coupling regime, and that diagrammatic resummation techniques are unlikely to be appropriate.Comment: 26 pages, two figures, LaTex macropackage. References added and appendix A revised. LBL preprint LBL-3457

Chiral Symmetry in Two-Color QCD at Finite Temperature

We study the chiral symmetry in two-color QCD with N massless flavors at finite temperature, using an effective theory. For the gauge group SU(2), the chiral symmetry is enlarged to SU(2N), which is then spontaneously broken to Sp(2N) at zero temperature. At finite temperature, and when the axial anomaly can be neglected, we find a first order phase transition occurring for two or more flavors. In the presence of instantons, the symmetry restoration unambiguously remains first order for three or more massless flavors. These results could be relevant for lattice studies of chiral symmetry at finite temperature and density.Comment: 10 pages, Revte

Proposal for a Constant Cosmological Constant

It is proposed that the apparent positive acceleration of the cosmological scale factor is due to the vacuum energy of an incomplete chiral phase transition in a hidden SU(2) sector. Constraints from primordial nucleosynthesis imply that the present metastable phase is in a substantially supercooled state. It is argued that massless chiral condensates can substantially enhance the possibility of supercooling, and a linear sigma model exhibiting scale invariance broken only at the quantum level is shown to accommodate the required supercooling with a reasonable choice of quartic couplings. The extensive supercooling can in principle be confirmed or rejected on the basis of interface tension measurements in lattice simulations with dynamical fermions.Comment: 12 pages, LaTeX, 1 figure; minor rewriting, references corrected, results unchange

New Universality Classes for Quantum Critical Behavior

We use the epsilon expansion to explore a new universality class of second order quantum phase transitions associated with a four-dimensional Yukawa field theory coupled to a traceless Hermitean matrix scalar field. We argue that this class includes four-fermi models in $2<D<4$ dimensions with $SU(N_F)\times U(N)$ symmetry and a U(N) scalar, $SU(N_F)$ iso-vector 4-fermi coupling. The epsilon expansion indicates that there is a second order phase transition for $N\geq N^*(N_F)$, where $N^*(N_F)\simeq.27N_F$ if $N_F\to\infty$.Comment: LaTeX, 9 pages, 1 tarred and uuencoded postscript figure. The new version contains information on the asymptotic dependence of the critical number of fermion species on $N_F

Phase transitions in quantum chromodynamics

The current understanding of finite temperature phase transitions in QCD is reviewed. A critical discussion of refined phase transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in effective continuum models for QCD is presented. Theoretical predictions about the order of the transitions are compared with possible experimental manifestations in heavy-ion collisions. Various places in phenomenological descriptions are pointed out, where more reliable data for QCD's equation of state would help in selecting the most realistic scenario among those proposed. Unanswered questions are raised about the relevance of calculations which assume thermodynamic equilibrium. Promising new approaches to implement nonequilibrium aspects in the thermodynamics of heavy-ion collisions are described.Comment: 156 pages, RevTex. Tables II,VIII,IX and Fig.s 1-38 are not included as postscript files. I would like to ask the requestors to copy the missing tables and figures from the corresponding journal-referenc