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 ν=0.63 and scalar and fermionic anomalous dimensions η_σ=0.31 and η_ψ=0.11, respectively. We also compute critical exponents for other N. Our results are based on exact renormalization-group equations.