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

The Lattice Fermi Surface

The Nambu - Jona-Lasinio model in 2+1 dimensions is simulated for non-zero baryon chemical potential with a diquark source term. No evidence for a BCS condensate or gap is seen at high density; rather, critical behaviour with novel exponents is observed, suggesting that 2d superfluidity as first described by Kosterlitz and Thouless is realised, but with the universality class determined by the presence of relativistic fermions.Comment: 5 pages, 5 figures, contribution to "Statistical QCD", Bielefeld, 26th-30th August 200

Simulating Dense Matter

I review the Sign Problem hindering lattice QCD simulations of dense baryonic matter, focussing where possible on its physical relevance. The possibility of avoiding the Sign Problem via a duality transformation is also briefly considered. Finally, I review evidence for deconfinement at non-zero quark density in recent simulations of Two Color QCD.Comment: Talk at "New Frontiers in QCD", Yukawa International Seminar 2006 (Kyoto), 8 pages, 7 figure

Quantum Critical Behaviour in a Graphene-like Model

We present the first results of numerical simulations of a 2+1 dimensional fermion field theory based on a recent proposal for a model of graphene, consisting of N_f four-component Dirac fermions moving in the plane and interacting via an instantaneous Coulomb interaction. In the strong-coupling limit we identify a critical number of flavors N_fc=4.8(2) separating an insulating from a conducting phase. This transition corresponds to the location of a quantum critical point, and we use a fit to the equation of state for the chiral order parameter to estimate the critical exponents. Next we simulate N_f=2 corresponding to real graphene, and approximately locate a transition from strong to weak coupling behaviour. Strong correlations are evident in the weak-coupling regime.Comment: 14 pages, 6 figure

Two Color Matter in the Quenched Approximation

We study a quenched SU(2) lattice gauge theory in 4d in which the spatial gauge ensemble $\{U_i\}$ is generated from a 3d gauge-Higgs model and the timelike link variables are ``reconstructed'' from the Higgs fields. The resulting ensemble is used to study quenched quark propagation with non-zero chemical potential $\mu$. 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: 7 pages, 4 figures; Poster presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German