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

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