  We study the double scaling limit of mKdV type, realized in the two-cut
Hermitian matrix model. Building on the work of Periwal and Shevitz and of
Nappi, we find an exact solution including all odd scaling operators, in terms
of a hierarchy of flows of $2\times 2$ matrices. We derive from it loop
equations which can be expressed as Virasoro constraints on the partition
function. We discover a ``pure topological" phase of the theory in which all
correlation functions are determined by recursion relations. We also examine
macroscopic loop amplitudes, which suggest a relation to 2D gravity coupled to
dense polymers.
