  We investigate numerically on the lattice the interplay of universality
classes of the three-dimensional Yukawa model with U(1) chiral symmetry, using
the Binder method of finite size scaling. At zero Yukawa coupling the scaling
related to the magnetic Wilson--Fisher fixed point is confirmed. At
sufficiently strong Yukawa coupling the dominance of the chiral fixed point
associated with the 3D Gross--Neveu model is observed for various values of the
coupling parameters, including infinite scalar selfcoupling. In both cases the
Binder method works consistently in a broad range of lattice sizes. However,
when the Yukawa coupling is decreased the finite size behavior gets complicated
and the Binder method gives inconsistent results for different lattice sizes.
This signals a cross-over between the universality classes of the two fixed
points.
