Branched Polymers with Loops

TL;DR

This paper classifies critical behaviors of branched polymers with arbitrary topology, demonstrating universality in their partition function's singular part and exploring connections to quantum gravity.

Contribution

It introduces a universal classification scheme for branched polymers' critical behaviors and provides exact and perturbative calculations of their partition functions.

Findings

Partition function's singular part is universal in a double scaling limit

Exact calculation of the partition function in the generic case

Perturbative calculation for non-generic cases

Abstract

We propose a classification of critical behaviours of branched polymers for arbitrary topology. We show that in an appropriately defined double scaling limit the singular part of the partition function is universal. We calculate this partition function exactly in the generic case and perturbatively otherwise. In the discussion section we comment on the relation between branched polymer theory and Euclidean quantum gravity.