Two-matrix model with ABAB interaction

Using recently developed methods of character expansions we solve exactly in the large N limit a new two-matrix model of hermitian matrices A and B with the action S = 1/2 (tr A(2) + tr B-2) - alpha/4 (tr A(4) + tr B-4) - beta/2 tr(AB)(2). This model can be mapped onto a special case of the 8-vertex model on dynamical planar graphs. The solution is parametrized in terms of elliptic functions. A phase transition is found: the critical point is a conformal field theory with central charge c = 1 coupled to 2D quantum gravity. (C) 1999 Published by Elsevier Science B.V.