Compressed self-avoiding walks in two and three dimensions

TL;DR

This paper investigates the phase transition of self-avoiding walks under compression in two and three dimensions, revealing how the polymer's behavior changes when confined between walls and analyzing the critical exponents through scaling and simulations.

Contribution

It introduces a new analysis of the phase transition in compressed self-avoiding walks, highlighting the lower-dimensional behavior of the compressed state and validating predictions with simulations.

Findings

Identification of phase transition characteristics under compression

Scaling exponents for the transition and compressed state

Agreement between theoretical predictions and Monte Carlo results

Abstract

We consider the phase transition induced by compressing a self-avoiding walk in a slab where the walk is attached to both walls of the slab in two and three dimensions, and the resulting phase once the polymer is compressed. The process of moving between a stretched situation where the walls pull apart to a compressed scenario is a phase transition with some similarities to that induced by pulling and pushing the end of the polymer. However, there are key differences in that the compressed state is expected to behave like a lower dimensional system, which is not the case when the force pushes only on the endpoint of the polymer. We use scaling arguments to predict the exponents both of those associated with the phase transition and those in the compressed state and find good agreement with Monte Carlo simulations.