Phase transition in fluctuating branched geometry

Abstract

We study grand--canonical and canonical properties of the model of branched polymers proposed in \cite{adfo}. We show that the model has a fourth order phase transition and calculate critical exponents. At the transition the exponent $\gamma$ of the grand-canonical ensemble, analogous to the string susceptibility exponent of surface models, $\gamma \sim \mathrm{0.3237525...}$ is the first known example of positive $\gamma$ which is not of the form $1/n,n=2,3,\dots$. We show that a slight modification of the model produces a continuos spectrum of $\gamma$'s in the range $(0,1/2]$ and changes the order of the transition.

Comments: 11 pages, requires Latex2e + psfrag.sty (supplied) + elsart.cls (supplied). 3 figures included as eps files