Lattice Study of Dense Matter with Two Colors and Four Flavors

We present results from a simulation of SU(2) lattice gauge theory with N_f=4 flavors of Wilson fermion and non-zero quark chemical potential mu, using the same 12^3x24 lattice, bare gauge coupling, and pion mass in cut-off units as a previous study with N_f=2. The string tension for N_f=4 is found to be considerably smaller implying smoother gauge field configurations. Thermodynamic observables and order parameters for superfluidity and color deconfinement are studied, and comparisons drawn between the two theories. Results for quark density and pressure as functions of mu are qualitatively similar for N_f=2 and N_f=4; in both cases there is evidence for a phase in which baryonic matter is simultaneously degenerate and confined. Results for the stress-energy tensor, however, suggest that while N_f=2 has a regime where dilute matter is non-relativistic and weakly-interacting, N_f=4 matter is relativistic and strongly-interacting for all values of mu above onset.Comment: Horizontal axes of several figures rescaled. Version accepted for publicatio

Application of the Maximum Entropy Method to the (2+1)d Four-Fermion Model

We investigate spectral functions extracted using the Maximum Entropy Method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma and massive pseudoscalar meson; our results confirm the Goldstone nature of the pi and permit an estimate of the meson binding energy. We have, however, seen no signal of sigma -> pi pi decay as the chiral limit is approached. In the symmetric phase we observe a resonance of non-zero width in qualitative agreement with analytic expectations; in addition the ultra-violet behaviour of the spectral functions is consistent with the large non-perturbative anomalous dimension for fermion composite operators expected in this model.Comment: 25 pages, 13 figure

The Universlity Class of Monopole Condensation in Non-Compact, Quenched Lattice QED

Finite size scaling studies of monopole condensation in noncompact quenched lattice $QED$ indicate an authentic second order phase transition lying in the universality class of four dimensional percolation. Since the upper critical dimension of percolation is six, the measured critical indices are far from mean-field values. We propose a simple set of ratios as the exact critical indices for this transition. The implication of these results for critical points in Abelian gauge theories are discussed.Comment: ILL-(TH)-92-6, CERN-TH.6515/92, 10 pages, no figures available as PS fil

Numerical Portrait of a Relativistic Thin Film BCS Superfluid

We present results of numerical simulations of the 2+1d Nambu - Jona-Lasinio model with a non-zero baryon chemical potential mu including the effects of a diquark source term. Diquark condensates, susceptibilities and masses are measured as functions of source strength j. The results suggest that diquark condensation does not take place in the high density phase mu>mu_c, but rather that the condensate scales non-analytically with j implying a line of critical points and long range phase coherence. Analogies are drawn with the low temperature phase of the 2d XY model. The spectrum of the spin-1/2 sector is also studied yielding the quasiparticle dispersion relation. There is no evidence for a non-zero gap; rather the results are characteristic of a normal Fermi liquid with Fermi velocity less than that of light. We conclude that the high density phase of the model describes a relativistic gapless thin film BCS superfluid.Comment: 37 pages, 16 figure

Mesonic Wavefunctions in the three-dimensional Gross-Neveu model

We present results from a numerical study of bound state wavefunctions in the (2+1)-dimensional Gross-Neveu model with staggered lattice fermions at both zero and nonzero temperature. Mesonic channels with varying quantum numbers are identified and analysed. In the strongly coupled chirally broken phase at T=0 the wavefunctions expose effects due to varying the interaction strength more effectively than straightforward spectroscopy. In the weakly coupled chirally restored phase information on fermion - antifermion scattering is recovered. In the hot chirally restored phase we find evidence for a screened interaction. The T=0 chirally symmetric phase is most readily distinguished from the symmetric phase at high T via the fermion dispersion relation.Comment: 18 page

The (2+1)-dimensional Gross-Neveu model with a U(1) chiral symmetry at non-zero temperature

We present results from numerical simulations of the (2+1)-dimensional Gross-Neveu model with a U(1) chiral symmetry and N_f=4 fermion species at non-zero temperature. We provide evidence that there are two different chirally symmetric phases, one critical and one with finite correlation length, separated by a Berezinskii-Kosterlitz-Thouless transition. We have also identified a regime above the critical temperature in which the fermions acquire a screening mass even in the absence of chiral symmetry breaking, analogous to the pseudogap behaviour observed in cuprate superconductors.Comment: 12 pages, 6 figure

Numerical Portrait of a Relativistic BCS Gapped Superfluid

We present results of numerical simulations of the 3+1 dimensional Nambu - Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the introduction of a chemical potential mu not equal to 0. The triviality of the model with a number of dimensions d>=4 is dealt with by fitting low energy constants, calculated analytically in the large number of colors (Hartree) limit, to phenomenological values. Non-perturbative measurements of local order parameters for superfluidity and their related susceptibilities show that, in contrast to the 2+1 dimensional model, the ground-state at high chemical potential and low temperature is that of a traditional BCS superfluid. This conclusion is supported by the direct observation of a gap in the dispersion relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15% the size of the vacuum fermion mass. We also present results of an initial investigation of the stability of the BCS phase against thermal fluctuations. Finally, we discuss the effect of splitting the Fermi surfaces of the pairing partners by the introduction of a non-zero isospin chemical potential.Comment: 41 pages, 19 figures, uses axodraw.sty, v2: minor typographical correction

The Four-Fermi Model in Three Dimensions at Non-Zero Density and Temperature

The Four Fermi model with discrete chiral symmetry is studied in three dimensions at non-zero chemical potential and temperature using the Hybrid Monte Carlo algorithm. The number of fermion flavors is chosen large $(N_f=12)$ to compare with analytic results. A first order chiral symmetry restoring transition is found at zero temperature with a critical chemical potential $\mu_c$ in good agreement with the large $N_f$ calculations. The critical index $\nu$ of the correlation length is measured in good agreement with analytic calculations. The two dimensional phase diagram (chemical potential vs. temperature) is mapped out quantitatively. Finite size effects on relatively small lattices and non-zero fermion mass effects are seen to smooth out the chiral transition dramatically.Comment: 21 pages, sorry, no figure

QCD at non-zero temperature and density from the lattice

The study of systems as diverse as the cores of neutron stars and heavy-ion collision experiments requires the understanding of the phase structure of QCD at non-zero temperature, T, and chemical potential, mu_q. We review some of the difficulties of performing lattice simulations of QCD with non-zero mu_q, and outline the re-weighting method used to overcome this problem. This method is used to determine the critical endpoint of QCD in the (mu_q,T) plane. We study the pressure and quark number susceptibility at small mu_q.Comment: 5 pages, talk presented by C.R. Allton at the QCD Downunder Conference, Barossa Valley and Adelaide, March 200

Infrared cutoff dependence of the critical flavor number in three-dimensional QED

We solve, analytically and numerically, a gap equation in parity invariant QED_3 in the presence of an infrared cutoff \mu and derive an expression for the critical fermion number N_c as a function of \mu. We argue that this dependence of N_c on the infrared scale might solve the discrepancy between continuum Schwinger-Dyson equations studies and lattice simulations of QED_3.Comment: 5 pages, 1 figure (revtex4), final versio