Yang-Lee zeros of the Ising model on random graphs of non planar topology

We obtain in a closed form the 1/N-2 contribution to the free energy of the two Hermitian N x N random matrix model with nonsymmetric quartic potentia l. From this result, we calculate numerically the Yang-Lee zeros of the 2D Ising model on dynamical random graphs with the topology of a torus up to n = 16 vertices. They are found to be located on the unit circle on the comp lex fugacity plane. In order to include contributions of even higher topolo gies we calculated analytically the nonperturbative (sum over all genus) pa rtition function of the model Z(n) = Sigma(h=0)(infinity) Z(n)((h))/N-2h fo r the special cases of N = 1,2 and graphs with n less than or equal to 20 v ertices. Once again the Yang-Lee zeros are shown numerically to lie on the unit circle on the complex fugacity plane. Our results thus generalize prev ious numerical results on random graphs by going beyond the planar approxim ation and strongly indicate that there might be a generalization of the Lee -Yang circle theorem for dynamical random graphs. (C) 2000 Elsevier Science B.V. All rights reserved.