A Monte Carlo study of the Gross-Neveu model

Several lattice versions of the Gross-Neveu model are constructed and studied using Monte Carlo methods. The expected shiral structures are confirmed by the numerical results. The correct asymptotic freedom behaviour is recovered with the appropriate number of species taken into account. The models differ in their number of soft modes and their strong coupling behaviour. In some of them, chiral symmetry is restored at a finite coupling. The large-N, finite-temperature transition is also found in good agreement with the theoretical value.