# Phase transition in fluctuating branched geometry

## TL;DR

This paper investigates a branched polymer model revealing a unique fourth-order phase transition with a positive string susceptibility exponent, and explores how modifications affect the spectrum of critical exponents and transition order.

## Contribution

It identifies a novel phase transition in a branched polymer model with a positive critical exponent not of the form 1/n, and examines how model modifications alter the spectrum of exponents and transition order.

## Key findings

- The model exhibits a fourth-order phase transition.
- The critical exponent γ is approximately 0.324, a novel positive value not of the form 1/n.
- Modifications lead to a continuous spectrum of γ in (0, 1/2] and change the transition order.

## 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, $\gamma \sim 0.3237525...$ is the first known example of positive $\gamma$ which is not of the form $1/n,\, n=2,3,\ldots$. 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.