  We investigate the Yukawa model in which $N_f$ fermions are coupled with a
scalar field $\phi$ through a Yukawa interaction. The phase diagram is rather
well understood. If the fermions are massless, there is a chiral transition at
$T_c$: for $T < T_c$ chiral symmetry is spontaneously broken. At $N_f=\infty$
the transition is mean-field like, while, for any finite $N_f$, standard
arguments predict Ising behavior. This apparent contradiction has been
explained by Kogut et al., who showed by scaling arguments and Monte Carlo
simulations that in the large-$N_f$ limit the width of the Ising critical
region scales as a power of $1/N_f$, so that only mean-field behavior is
observed for $N_f$ strictly equal to infinity. We will show how the results of
Kogut et al. can be recovered analytically in the framework of a generalized
$1/N_f$ expansion. The method we use is a simple generalization of the method
we have recently applied to a two-dimensional generalized Heisenberg model.
