Comment on `Stretched polymers in a poor solvent'

TL;DR

This paper critiques existing scaling theories for stretched polymers in poor solvents, clarifying crossover behaviors and thermal exponents near the $ heta$-point in low-dimensional systems.

Contribution

It provides a detailed summary of crossover theory and clarifies the relationship between thermal exponents approaching the $ heta$-point in low dimensions.

Findings

Clarified the scaling arguments near the $ heta$-point.

Summarized crossover theory predictions for low-dimensional systems.

Connected thermal exponents with asymptotic behaviors at the $ heta$-point.

Abstract

In a recent article on stretched polymers in a poor solvent by Grassberger and Hsu \cite{grassberger2002a-a} questions were raised as to the conclusions that can be drawn from currently proposed scaling theory for a single polymer in various types of solution in two and three dimensions. Here we summarise the crossover theory predicted for low dimensions and clarify the scaling arguments that relate thermal exponents for quantities on approaching the $\theta$-point from low temperatures to those associated with the asymptotics in polymer length at the $\theta$-point itself.