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 $〈\mathrm{qq}〉$ 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 $〈\mathrm{qq}〉\propto j^{\alpha }$ 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 $E\left(k\right)$ 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 ${\Sigma }_0$.