  We consider a two matrix model with gaussian interaction involving the term
$tr ABAB$, which is quartic in angular variables. It describes a vertex model
(in particular case - of F-model type) on the lattice of fluctuating geometry
and is the simplest representative of the class of matrix models describing
coupling to two-dimensional gravity of general vertex models. This class
includes most of physically interesting matrix models, such as lattice gauge
theories and matrix models describing extrinsic curvature strings. We show that
the system of loop (Schwinger-Dyson) equations of the model decouples in the
planar limit and allows one to find closed equations for arbitrary correlators,
including the ones involving angular variables. This provides a solution of the
model in the planar limit. We write down the equations for the two-point
function and the eigenvalue density and sketch the calculation of perturbative
corrections to the free case.
