  We present a new solution of the asymmetric two-matrix model in the large $N$
limit which only involves a saddle point analysis. The model can be interpreted
as Ising in the presence of a magnetic field, on random dynamical lattices with
the topology of the sphere (resp. the disk) for closed (resp. open) surfaces;
we elaborate on the resulting phase diagram. The method can be equally well
applied to a more general $(Q+1)$-matrix model which represents the dilute
Potts model on random dynamical lattices. We discuss in particular duality of
boundary conditions for open random surfaces.
