THE YANG–LEE EDGE SINGULARITY ON A DYNAMICAL PLANAR RANDOM SURFACE

Abstract

We reconsider a recently solved Ising model on a random planar graph . The Yang-Lee edge singularity, familiar from the ordinary Ising model, is exposed . It is shown to correspond to an exactly solvable critical dimer counting problem on the random surface in the infinite temperature limit. This suggests an interesting interpretation of a recently proposed phenomenological model exhibiting multicritical behavior. The critical exponents are found to be y= 3 (string susceptibility) and a = '-, (edge singularity). The result is at odds with the Knizhnik-Polyakov-Zamolodchikov formula in conjunction with the Yang-Lee edge singularity's central charge C= sz . Possible explanations are discussed . The result a= z coincides with the corresponding exponent of the ordinary three-dimensional spherical model, as does the set of exponents of the random [sing critical point found previously .