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

We present results of a Monte Carlo simulation of a (2 + 1)-dimensional Nam bu-Jona-Lasinio model. In the vacuum phase, the diquark condensate [qq] van ishes linearly as a function of diquark source j as expected, but simulatio ns in a region with nonzero baryon density suggest a power-law scaling [qq] proportional to j(alpha) and hence a critical system for all mu > mu (c). There is no signal for superfluidity. Comparisons are drawn with the pseudo gap phase in cuprate superconductors. We also measure the dispersion relati on 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 const ituent quark mass scale Sigma (0).