Monopole Percolation and The Universality Class of the Chiral Transition in Four Flavor Noncompact Lattice QED

We simulate four flavor noncompact lattice QED using the Hybrid Monte Carlo algorithm on $10^4$ and $16^4$ lattices. Measurements of the monopole susceptibility and the percolation order parameter indicate a transition at $\beta = {1/e^2} = .205(5)$ with critical behavior in the universality class of four dimensional percolation. We present accurate chiral condensate measurements and monitor finite size effects carefully. The chiral condensate data supports the existence of a power-law transition at $\beta = .205$ in the same universality class as the chiral transition in the two flavor model. The resulting equation of state predicts the mass ratio $m_\pi^2/m_\sigma^2$ in good agreement with spectrum calculations while the hypothesis of a logarithmically improved mean field theory fails qualitatively.Comment: 17 pages, 10 figure

Phase diagram of the three-dimensional NJL model

With the exception of confinement the three-dimensional Nambu-Jona-Lasinio (NJL_3) model incorporates many of the essential properties of QCD. We discuss the critical properties of the model at nonzero temperature T and/or nonzero chemical potential $\mu$. We show that the universality class of the thermal transition is that of the d=2 classical spin model with the same symmetry. We provide evidence for the existence of a tricritical point in the ($\mu$,temperature) plane. We also discuss numerical results by Hands et al. which showed that the system is critical for $\mu>\mu_c$ and the diquark condensate is zero.Comment: 3 pages, To appear in the proceedings of Conference on Quarks and Nuclear Physics (QNP 2002), Julich, Germany, 9-14 Jun 200

Improving the Lattice QED Action

Strongly coupled QED is a model whose physics is dominated by short-ranged effects. In order to assess which features of numerical simulations of the chiral phase transition are universal and which are not, we have formulated a quenched version of the model in which photon degrees of freedom are defined on a lattice of spacing a, but fermions only on a lattice of spacing 2a. The fermi-photon interaction is then obtained via a blocking procedure, whose parameters allow a degree of control over the relative importance of short wavelength modes. Results from a variety of models are presented; the critical exponents delta and beta governing the transition appear to be independent of the blocking, or even of whether a gauge-invariant action is used for the photons.Comment: 3 pages LaTeX submission to Lat' 94 proceedings, 3 PostScript figures incorporated using macro psfi

Evidence for BCS Diquark Condensation in the 3+1d Lattice NJL Model

We present results of numerical simulations of the 3+1d Nambu - Jona-Lasinio model with a non-zero baryon chemical potential mu, with particular emphasis on the superfluid diquark condensate and associated susceptibilities. The results, when extrapolated to the zero diquark source limit, are consistent with the existence of a non-zero BCS condensate at high baryon density. The nature of the infinite volume and zero temperature limits are discussed.Comment: 12 pages, 5 figure

Can we study Quark Matter in the Quenched Approximation?

We study a quenched SU(2) lattice gauge theory in which, in an attempt to distinguish between timelike and spacelike gauge fields, the gauge ensemble {U_mu} is generated from a 3 dimensional gauge-Higgs model, the timelike link variables being "reconstructed" from the Higgs fields. The resulting ensemble is used to study quenched quark propagation with non-zero chemical potential mu; in particular, the quark density, chiral and superfluid condensates, meson, baryon and gauge-fixed quark propagators are all studied as functions of mu. While it proves possible to alter the strength of the inter-quark interaction by changing the parameters of the dimensionally reduced model, there is no evidence for any region of parameter space where quarks exhibit deconfined behaviour or thermodynamic observables scale as if there were a Fermi surface.Comment: 31 pages, 20 figures, enhanced discussion and analysis of finite volume effects, version accepted for publication by Nucl. Phys.

Supercurrent Flow in NJL_{2+1} at High Baryon Density

We present results of numerical simulations of the 2+1d Nambu -- Jona-Lasinio model with non-zero baryon chemical potential mu and spatially-varying complex diquark source strength j. By choosing arg(j) to vary smoothly through 2 pi across the spatial extent of the lattice, a baryon number current is induced which in the high density phase remains non-vanishing as |j|->0; we are hence able to extract a quantity characteristic of a superfluid known as the helicity modulus. We also study supercurrent flow at non-zero temperature and estimate the critical temperature at which the normal phase is restored, which is consistent with the conventional picture for thin-film superfluids in which the transition is viewed in terms of vortex -- anti-vortex unbinding.Comment: 10 pages, 5 figure

Hadron Spectrum in a Two-Colour Baryon-Rich Medium

The hadron spectrum of SU(2) lattice gauge theory with two flavours of Wilson quark is studied on an 8^3x16 lattice using all-to-all propagators, with particular emphasis on the dependence on quark chemical potential mu. As mu is increased from zero the diquark states with non-zero baryon number B respond as expected, while states with B=0 remain unaffected until the onset of non-zero baryon density at mu=m_pi/2. Post onset the pi-meson mass increases in accordance with chiral perturbation theory while the rho becomes lighter. In the diquark sector a Goldstone state associated with a superfluid ground state can be identified. A further consequence of superfluidity is an approximate degeneracy between mesons and baryons with the same spacetime and isospin quantum numbers. Finally we find tentative evidence for the binding of states with kaon quantum numbers within the baryonic medium.Comment: 14 pages, 5 figure

Magnetic Monopoles in non-compact QED - is there a Phase Transition?

The existence of the monopole condensation transition reported by Kocic et al. in non-compact, quenched QED is tested. No phase transition is found. This shows that divergence of the `monopole susceptibility' introduced by Hands and Wensley is not a reliable indicator of second order phase transitions. In view of these results I discuss claims that the chiral phase transition seen in QED with fermions is a lattice artefact driven by monopole condensation.Comment: Talk given at lattice '92, 4 pages, uses espcrc2.sty, 2 postscript figures attached. (Replaced to add the figures.) Preprint FUB-HEP 22/9

A BCS Gap on the Lattice

Monte Carlo simulations of the 3+1 dimensional NJL model are performed with baryon chemical potential mu>0. For mu>Sigma_0, the constituent quark mass in vacuum, chiral symmetry is restored and a diquark condensate forms. We analyse the fermion propagator and find evidence for particle-hole mixing in the vicinity of the Fermi surface and an energy gap Delta>0, both of which provide evidence for superfluidity at high baryon density induced by a BCS mechanism. At (mu a)=0.8 the ratio between the BCS gap and the vacuum quark mass is Delta/Sigma_0=0.15(2).Comment: 3 pages, 3 figures, Lattice2003(nonzero

Diquark condensation in dense SU(2) matter

We report on a lattice study of two-color QCD with adjoint staggered fermions at high density. We find that the model has no early onset and we report on results for diquark condensation, from simulations with and without a diquark source term.Comment: Lattice2001(hightemp