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 γ = − 1 3 (string susceptibility) and σ = 1 2 (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 = − 22 5 . Possible explanations are discussed. The result σ = 1 2 coincides with the corresponding exponent of the ordinary three-dimensional spherical model, as does the set of exponents of the random Ising critical point found previously.