Branched Polymers Re-Revisited

TL;DR

This paper clarifies misconceptions about the behavior of two-point functions in branched polymers, correcting previous claims and reaffirming their known Hausdorff dimension of four.

Contribution

It refutes a recent claim about the two-point function behavior in branched polymers and clarifies the relationship with their Hausdorff dimension.

Findings

The two-point function behaves as 1/p^2 for large p.

The Hausdorff dimension of branched polymers remains four.

Previous claims of 1/p^4 behavior are incorrect.

Abstract

We point out some misconceptions in a recent paper by H. Aoki et al. [hep-th/9909060]. In particular, the claim that the two-point function of branched polymers behaves as 1/p^4 instead of 1/p^2 for large p is mistaken and in no way a precondition for the Hausdorff dimension of branched polymers having the well known value four.