The Nambu-Jona-Lasinio model reduced to $2+1$ dimensions has two different path integral formulations: at finite chemical potential one formulation has a severe sign problem similar to that found in QCD, while the other does not. At large $N$, where $N$ is the number of flavors, one can compute the probability distributions of fermion correlators analytically in both formulations. In the former case one finds a broad distribution with small mean; in the latter one finds a heavy tailed positive distribution amenable to the cumulant expansion techniques developed in earlier work. We speculate on the implications of this model for QCD.

• Received 6 September 2012

DOI:https://doi.org/10.1103/PhysRevD.87.014504