Weighting of topologically different interactions in a model of two-dimensional polymer collapse

TL;DR

This study uses computer simulations to analyze a generalized two-dimensional polymer model distinguishing crossings and collisions, confirming that asymmetry in interactions does not alter the universality class unless crossings dominate, which reverts to classical behavior.

Contribution

It introduces and investigates a generalized self-interacting trail model with topologically different interactions, confirming the robustness of the universality class under certain asymmetries.

Findings

Asymmetry does not affect the universality class for a range of parameters.

Heavy weighting of collisions leads to classical theta-point behavior.

The model generalizes the canonical polymer collapse model with topological distinctions.

Abstract

We study by computer simulation a recently introduced generalised model of self-interacting self-avoiding trails on the square lattice that distinguishes two topologically different types of self-interaction: namely crossings where the trail passes across itself and collisions where the lattice path visits the same site without crossing. This model generalises the canonical interacting self-avoiding trail model of polymer collapse which has a strongly divergent specific heat at its transition point. We confirm the recent prediction that the asymmetry does not affect the universality class for a range of asymmetry. Certainly, where the weighting of collisions outweighs that of crossings this is well supported numerically. When crossings are weighted heavily relative to collisions the collapse transition reverts to the canonical theta-point-like behaviour found in interacting self-avoiding walks.