The U(1) Gross-Neveu Model at Non-Zero Chemical Potential

The four-fermi model with continuous chiral symmetry is studied in three dimensions at non-zero chemical potential $\mu$ using both the $1/N_f$ expansion and computer simulations. For strong coupling this model spontaneously breaks its U(1) chiral symmetry at zero chemical potential and the Goldstone mechanism is realized through massless pions. The computer simulation predicts a critical chemical potential $\mu_c$ close to the lightest fermion mass in the model. As $\mu$ is increased beyond $\mu_c$, the pion screening mass increases rapidly from zero to a nonvanishing value indicating symmetry restoration. Some lessons are drawn relevant to lattice QCD simulations at non-zero $\mu$.