  A model is proposed which can be regarded as a mean field approximation for
pure lattice QCD and chiral field. It always possesses a phase transition
between a strong coupling phase (where it reduces to a one-plaquette integral)
and a non-trivial weak coupling one. For the U(N) gauge group, it is equivalent
to some multi-matrix model. This analogy allows for determining possible large
N critical regimes thus generalizing the Gross-Witten phase transition in the
one-plaquetee model.
