On the equivalence between 2D Yukawa and Gross-Neveu models

Abstract

We study numerically on the lattice the 2D Yukawa model with the U(1) chiral symmetry and N F = 16 at infinite scalar field self-coupling. The scaling behaviour of the fermion mass, as the Yukawa coupling approaches zero, is analysed using the mean field method. It is found to agree with that of the Gross-Neveu model with the same symmetry and N F . This suggests that the 2D Yukawa sign of the bare kinetic term of the scalar field is negative. This suggests that the 2D Yukawa models belong to the universality class of the Gross-Neveu models not only at weak scalar field self-coupling but also for a broad range of the bare parameters which is not accessible to the 1/ N F expansion. New universality classes might arise at the crossover to the spin model universality class, however.