  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 $N_F$. The results suggest 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.
