The Spectral Dimension of Non-generic Branched Polymer Ensembles

TL;DR

This paper derives the spectral dimension of non-generic branched polymer models, revealing it depends on the susceptibility exponent and is 2 for models with negative gamma.

Contribution

It provides an exact formula for the spectral dimension of non-generic branched polymers based on the susceptibility exponent gamma.

Findings

Spectral dimension equals 2/(1+gamma) for models with positive gamma.

Spectral dimension is 2 for models with negative gamma.

The results connect spectral properties with the susceptibility exponent.

Abstract

We show that the spectral dimension on non-generic branched polymer models with susceptibility exponent $\gamma$ is given by $2/(1+\gamma)$. For those models with negative $\gamma$ we find that the spectral dimension is 2.