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We study the double scaling limit of mKdV type, realized in the two-cutHermitian matrix model. Building on the work of Periwal and Shevitz and ofNappi, we find an exact solution including all odd scaling operators, in termsof a hierarchy of flows of $2\times 2$ matrices. We derive from it loopequations which can be expressed as Virasoro constraints on the partitionfunction. We discover a ``pure topological" phase of the theory in which allcorrelation functions are determined by recursion relations. We also examinemacroscopic loop amplitudes, which suggest a relation to 2D gravity coupled todense polymers.Comment: 24p

LOOP EQUATIONS AND THE TOPOLOGICAL PHASE OF MULTI-CUT MATRIX MODELS