The six-vertex model on random lattices

In this letter, the 6-vertex model on dynamical random lattices is defined via a matrix model and rewritten (following I. Kostov) as a deformation of the O(2) model. In the large-N planar limit, an exact solution is found at criticality. The critical exponents of the model are determined; they vary continuously along the critical line. The vicinity of the latter is explored, which confirms that we have a line of c = 1 conformal field theories coupled to gravity.