Exact solution of the six-vertex model on a random lattice

We solve exactly the 6-vertex model on a dynamical random lattice, using it s representation as a large N matrix model. The model describes a gas of de nse nonintersecting oriented loops coupled to the local curvature defects o n the lattice. The model can be mapped to the c = 1 string theory, compacti fied at some length depending on the vertex coupling. We give explicit expr ession for the disk amplitude and evaluate the fractal dimension of its bou ndary, the average number of loops and the dimensions of the vortex operato rs, which vary continuously with the vertex coupling. (C) 2000 Elsevier Sci ence B.V. All rights reserved.