Critical behavior in the dense planar Nambu--Jona-Lasinio model

We present results of a Monte Carlo simulation of a (2+1)-dimensional Nambu-Jona-Lasinio model. In the vacuum phase, the diquark condensate vanishes linearly as a function of diquark source j as expected, but simulations in a region with nonzero baryon density suggest a power-law scaling infinity j(alpha) and hence a critical system for all mu > mu(c). There is no signal for superfluidity. Comparisons are drawn 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 gap Delta is constrained to be much less than the constituent quark mass scale Sigma(0).