  We present results of numerical simulations of the 2+1d Nambu - Jona-Lasinio
model with a non-zero baryon chemical potential mu including the effects of a
diquark source term. Diquark condensates, susceptibilities and masses are
measured as functions of source strength j. The results suggest that diquark
condensation does not take place in the high density phase mu>mu_c, but rather
that the condensate scales non-analytically with j implying a line of critical
points and long range phase coherence. Analogies are drawn with the low
temperature phase of the 2d XY model. The spectrum of the spin-1/2 sector is
also studied yielding the quasiparticle dispersion relation. There is no
evidence for a non-zero gap; rather the results are characteristic of a normal
Fermi liquid with Fermi velocity less than that of light. We conclude that the
high density phase of the model describes a relativistic gapless thin film BCS
superfluid.
