Diquark and Pion Condensation in Random Matrix Models for two-color QCD

We introduce a random matrix model with the symmetries of QCD with two colors at nonzero isospin and baryon chemical potentials and temperature. We analyze its phase diagram and find phases with condensation of pion and diquark states in addition to the phases with spontaneously broken chiral symmetries. In the limit of small chemical potentials and quark masses, we reproduce the mean field results obtained from chiral Lagrangians. As in the case of QCD with three colors, the presence of two chemical potentials breaks the flavor symmetry and leads to phases that are characterized by different behaviors of the chiral condensates for each flavor. In particular, the phase diagram we obtain is similar to QCD with three colors and three flavors of quarks of equal masses at zero baryon chemical potential and nonzero isospin and strange chemical potentials. A tricritical point of the superfluid transitions found in lattice calculations and from an analysis in terms of chiral Lagrangians does not appear in the random matrix model. Remarkably, at fixed isospin chemical potential, for the regions outside of the superfluid phases, the phase diagram in the temperature - baryon chemical potential plane for two colors and three colors are qualitatively the same.Comment: 19 pages, 7 figures, RevTeX

The QCD Phase Diagram at Nonzero Temperature, Baryon and Isospin Chemical Potentials in Random Matrix Theory

We introduce a random matrix model with the symmetries of QCD at finite temperature and chemical potentials for baryon number and isospin. We analyze the phase diagram of this model in the chemical potential plane for different temperatures and quark masses. We find a rich phase structure with five different phases separated by both first and second order lines. The phases are characterized by the pion condensate and the chiral condensate for each of the flavors. In agreement with lattice simulations, we find that in the phase with zero pion condensate the critical temperature depends in the same way on the baryon number chemical potential and on the isospin chemical potential. At nonzero quark mass, we remarkably find that the critical end point at nonzero temperature and baryon chemical potential is split in two by an arbitrarily small isospin chemical potential. As a consequence, there are two crossovers that separate the hadronic phase from the quark-gluon plasma phase at high temperature. Detailed analytical results are obtained at zero temperature and in the chiral limit.Comment: 13 pages, 5 figures, REVTeX

An AC susceptometer for the characterization of large, bulk superconducting samples

The main purpose of this work was to design, develop and construct a simple, low-cost AC susceptometer to measure large, bulk superconducting samples (up to 32 mm in diameter) in the temperature range 78-120 K. The design incorporates a double heating system that enables a high heating rate (25 K/hour) while maintaining a small temperature gradient (< 0.2 K) across the sample. The apparatus can be calibrated precisely using a copper coil connected in series with the primary coil. The system has been used successfully to measure the temperature dependence of the AC magnetic properties of entire RE-Ba-Cu-O [(RE)BCO] bulk superconducting domains. A typical AC susceptibility measurement run from 78 K to 95 K takes about 2 hours, with excellent temperature resolution (temperature step ~ 4 mK) around the critical temperature, in particular.Comment: 25 pages, 7 figures. Accepted for publication in Measurement Science and Technolog

Massive quark propagator and competition between chiral and diquark condensate

The Green-function approach has been extended to the moderate baryon density region in the framework of an extended Nambu--Jona-Lasinio model, and the thermodynamic potential with both chiral and diquark condensates has been evaluated by using the massive quark propagator. The phase structure along the chemical potential direction has been investigated and the strong competition between the chiral and diquark condensate has been analyzed by investigating the influence of the diquark condensate on the sharp Fermi surface. The influence of the diquark condensate on the quark properties has been investigated, even though the quarks in the color breaking phase are very different from that in the chiral breaking phase, the difference between quarks in different colors is very small.Comment: Revtex, 34 pages, 7 figures, section V revised, accepted by PR

Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD

In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We calculate spectral correlation functions of complex eigenvalues using a random matrix model approach. Our results apply to non-Hermitian Dirac operators in three-dimensional QCD with broken flavor symmetry and in four-dimensional QCD in the bulk of the spectrum. The derivation follows earlier results of Fyodorov, Khoruzhenko and Sommers for complex spectra exploiting the existence of orthogonal polynomials in the complex plane. Explicit analytic expressions are given for all microscopic k-point correlation functions in the presence of an arbitrary even number of massive quarks, both in the limit of strong and weak non-Hermiticity. In the latter case the parameter governing the non-Hermiticity of the Dirac matrices is identified with the influence of the chemical potential

Flavor Diagonal and Off-Diagonal Susceptibilities in a Quasiparticle Model of the Quark-Gluon Plasma

The Taylor coefficients of flavor diagonal and off-diagonal susceptibilities as well as baryon number, isovector and electric charge susceptibilities are considered within a phenomenological quasiparticle model of the quark-gluon plasma and successfully compared with lattice QCD data for two degenerate quark flavors. These susceptibility coefficients represent sensible probes of baryon density effects in the equation of state. The baryon charge is carried, in our model, by quark-quasiparticle excitations for hard momenta.Comment: Jan 2008. 25 p

Solution to the 3-Loop Φ\Phi-Derivable Approximation for Massless Scalar Thermodynamics

We develop a systematic method for solving the 3-loop $\Phi$-derivable approximation to the thermodynamics of the massless $\phi^4$ field theory. The method involves expanding sum-integrals in powers of $g^2$ and m/T, where g is the coupling constant, m is a variational mass parameter, and T is the temperature. The problem is reduced to one with the single variational parameter m by solving the variational equations order-by-order in $g^2$ and m/T. At the variational point, there are ultraviolet divergences of order $g^6$ that cannot be removed by any renormalization of the coupling constant. We define a finite thermodynamic potential by truncating at $5^{th}$ order in g and m/T. The associated thermodynamic functions seem to be perturbatively stable and insensitive to variations in the renormalization scale.Comment: 57 pages, 10 figure

Meson Exchange Effect on Color Superconductivity

We investigate the effects of pion and gluon exchanges on the formation of two-flavor color superconductivity at moderate density, $\mu <1 GeV$. The chiral quark model proposed by Manohar and Georgi containing pions as well as gluons is employed to show that the pion exchange reduces substantially the value of the superconducting gap gotten with the gluon exchange only. It turns out that the pion exchanges produce a repulsion between quark-quark pair in a spin and isospin singlet state. We suggest that the phase consisiting of pions, gluons and quarks is one of the candidates of in-medium QCD phase at moderate density.Comment: 8 pages, 1 figure, minor correction

Thermodynamics of two-colour QCD and the Nambu Jona-Lasinio model

We investigate two-flavour and two-colour QCD at finite temperature and chemical potential in comparison with a corresponding Nambu and Jona-Lasinio model. By minimizing the thermodynamic potential of the system, we confirm that a second order phase transition occurs at a value of the chemical potential equal to half the mass of the chiral Goldstone mode. For chemical potentials beyond this value the scalar diquarks undergo Bose condensation and the diquark condensate is nonzero. We evaluate the behaviour of the chiral condensate, the diquark condensate, the baryon charge density and the masses of scalar diquark, antidiquark and pion, as functions of the chemical potential. Very good agreement is found with lattice QCD (N_c=2) results. We also compare with a model based on leading-order chiral effective field theory.Comment: 24 pages, 12 figure