Phase diagram of theN=2 Kazakov-Migdal model

We have determined the phase diagram of the simplest version of a lattice model recently introduced by Kazakov and Migdal. Denoting by ${\mathit{m}}_0$ and λ the mass and the coupling of the scalar field in the model, we find a line of first-order phase transitions in the (${\mathit{m}}_0$,λ) plane ending in a critical point where λ is nonzero. Kazakov and Migdal speculate that their model of scalar field theory could induce QCD. Our work indicates that there is no continuum limit except at the critical end point. Whether or not a nontrivial continuum limit exists, there requires a careful study of the renormalization-group properties of the model.