Phase transition and critical behavior of thed=3 Gross-Neveu model

A second-order phase transition for the three-dimensional Gross-Neveu model is established for one fermion species, $N=1.$ This transition breaks a paritylike discrete symmetry. It constitutes its peculiar universality class with critical exponent $\ensuremath{\nu}=0.63$ and scalar and fermionic anomalous dimensions ${\ensuremath{\eta}}_{\ensuremath{\sigma}}=0.31$ and ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.11,$ respectively. We also compute critical exponents for other N. Our results are based on exact renormalization-group equations.