Critical Behaviour in the Dense Planar NJL Model

We present results of a Monte Carlo simulation of a 2+1 dimensional Nambu - Jona-Lasinio model including diquark source terms. A diquark condensate <qq> is measured as a function of source strength j. In the vacuum phase <qq> vanishes linearly with j as expected, but simulations in a region with non-zero baryon density suggest a power-law scaling and hence a critical system for all mu > mu_c. There is no diquark condensation signalling superfluidity. Comparisons are drawn with known results in two dimensional theories, and with the pseudogap phase in cuprate superconductors. We also measure the dispersion relation E(k) for fermionic excitations, and find results consistent with a sharp Fermi surface. Any superfluid gap Delta is constrained to be much less than the constituent quark mass scale Sigma_0.