On Phase Transition of Two-Dimensional Topological Gravity

Abstract

We show that one can use some renormalized coupling constants to compute the free energy and correlation functions at all critical points of the two-dimensional topological gravity in a uniform way. In particular, one can derive the critical exponents of the free energy and correlation functions at all critical points in a uniform way. Some concrete results for the case of $(3,2)$-model (pure gravity) and the $(5,2)$-model (Yang-Lee edge singularity coupled with gravity) are also presented.