Nonperturbative solution of the Ising model on a random surface

Details Nonperturbative solution of the Ising model on a random surface Nonperturbative solution of the Ising model on a random surface

Feb 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phrvl..64..717g&link_type=abstract

Physical Review Letters, Volume 64, Issue 7, February 12, 1990, pp.717-720

Physics

195

Scientific paper

The two-matrix-model representation of the Ising model on a random surface is solved exactly to all orders in the genus expansion. The partition function obeys a fourth-order nonlinear differential equation as a function of the string coupling constant. This equation differs from that derived for the k=3 multicritical one-matrix model, thus disproving that this model describes the Ising model. A similar equation is derived for the Yang-Lee edge singularity on a random surface, and is shown to agree with the k=3 multicritical one-matrix model.

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