  We have determined the phase diagram of the simplest version of a lattice
model introduced in the recent work of Kazakov and Migdal. If $m_0$ and
$\lambda$ are the bare mass and self coupling of the scalar field in the model
respectively, we find a line of first order phase transitions in the ($m_0,
\lambda$) plane ending in a critical point where $\lambda$ is nonzero. Kazakov
and Migdal speculate that their model of scalar field theory could induce QCD.
Our work indicates that for $N=2$ there is no continuum limit for the
Kazakov-Migdal model except at the critical end point. Whether or not a
nontrivial continuum limit exists in the vicinity of the critical point
requires careful study of the renormalization group properties of the model.
