  We study by numerical simulation a lattice Yukawa model with naive fermions
at intermediate values of the Yukawa coupling $y$ when the nearest neighbour
coupling $\kp$ of the scalar field $\Phi$ is very weakly ferromagnetic ($\kp
\approx 0$) or even antiferromagnetic ($\kappa < 0$) and the nonvanishing value
of $\vev$ is generated by the Yukawa interaction. The renormalized Yukawa
coupling $y_R$ achieves here its maximal value and this $y$-region is thus of
particular importance for lattice investigations of strong Yukawa interaction.
However, here the scalar field propagators have a very complex structure caused
by fermion loop corrections and by the proximity of phases with
antiferromagnetic properties. We develop methods for analyzing these
propagators and for extracting the physical observables. We find that going
into the negative $\kp$ region, the scalar field renormalization constant
becomes small and $y_R$ does not seem to exceed the unitarity bound, making the
existence of a nontrivial fixed point in the investigated Yukawa model quite
unlikely.
