Polymer models with competing collapse interactions on Husimi and Bethe lattices

TL;DR

This paper studies a generalized polymer model on Husimi and Bethe lattices, unifying several known models and exploring their collapse transitions to shed light on the complex phase behavior of polymers.

Contribution

It introduces a mean-field framework that encompasses various polymer models, aiming to clarify the nature of collapse transitions and theta points in polymer phase diagrams.

Findings

Unified description of different polymer models.

Identification of collapse transition characteristics.

Insights into the role of theta points in phase behavior.

Abstract

In the framework of Husimi and Bethe lattices, we investigate a generalized polymer model that incorporates as special cases different models previously studied in the literature, namely, the standard interacting self-avoiding walk, the interacting self-avoiding trail, and the vertex-interacting self-avoiding walk. These models are characterized by different microscopic interactions, giving rise, in the two-dimensional case, to collapse transitions of an apparently different nature. We expect that our results, even though of a mean-field type, could provide some useful information to elucidate the role of such different theta points in the polymer phase diagram. These issues are at the core of a long-standing unresolved debate.