Branched polymers on branched polymers

TL;DR

This paper investigates a model of branched polymers embedded within other branched polymers, revealing a phase transition characterized by specific critical exponents relevant to matter-geometry interactions.

Contribution

It introduces a toy model for studying matter-geometry interactions and identifies a phase transition with unique critical behavior.

Findings

Phase transition occurs where embedded polymers cover the basis polymers.

At the transition, susceptibility exponent γ equals 3/4.

Two-point function exhibits an anomalous dimension of 1/2.

Abstract

We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of interest in the study of the interaction of matter and quantized gravity. We find a phase transition at which the embedded polymers begin to cover the basis polymers. At the phase transition point the susceptibility exponent $\gamma$ takes the value 3/4 and the two-point function develops an anomalous dimension 1/2.