Polymer models with competing collapse interactions on Husimi and Bethe lattices

Area of Science:

• Statistical Mechanics
• Polymer Physics
• Computational Physics

Background:

• Existing polymer models like self-avoiding walks exhibit diverse collapse transition behaviors.
• Understanding these transitions is crucial for polymer phase diagram elucidation.
• A unified framework is needed to compare different microscopic interaction effects.

Purpose of the Study:

• To investigate a generalized polymer model on Husimi and Bethe lattices.
• To unify and analyze standard interacting self-avoiding walk, interacting self-avoiding trail, and vertex-interacting self-avoiding walk models.
• To provide mean-field insights into polymer collapse transitions and their underlying mechanisms.

Main Methods:

• Utilizing the framework of Husimi and Bethe lattices.
• Developing a generalized polymer model encompassing various existing models.
• Applying mean-field theoretical approaches.

Main Results:

• The generalized model successfully incorporates diverse polymer models as special cases.
• Mean-field analysis suggests different natures for collapse transitions in 2D, depending on microscopic interactions.
• The study provides a theoretical basis for comparing distinct polymer collapse phenomena.

Conclusions:

• The generalized polymer model offers a unified perspective on self-avoiding walks.
• Mean-field results contribute to understanding the role of microscopic interactions in polymer collapse.
• Further research can build upon these findings to resolve long-standing debates in polymer physics.