Generalized interacting self-avoiding trails on the square lattice: phase diagram and critical behavior

Area of Science:

• Statistical mechanics
• Polymer physics
• Condensed matter physics

Background:

• Self-avoiding walks and trails are fundamental models in statistical physics.
• Understanding interactions and rigidity is crucial for modeling complex polymer systems.
• Existing models like the Nienhuis O(n=0) model offer insights but lack generalized interaction types.

Purpose of the Study:

• To present and analyze a generalized model for interacting self-avoiding trails on a square lattice.
• To incorporate distinct interaction types: on-site double visits (collisions) and crossings.
• To investigate the effect of rigidity on trail behavior and collapse phenomena.

Main Methods:

• Numerical transfer matrix methods were employed for simulation and analysis.
• The generalized model was systematically studied to observe emergent behaviors.
• Comparison with established models like the pure interacting self-avoiding trail model was performed.

Main Results:

• The generalized model successfully incorporates both collisions and crossings, alongside rigidity.
• The study demonstrates that the generic collapse behavior is consistent with the pure interacting self-avoiding trail model.
• The model provides a unified framework encompassing special cases like the Nienhuis O(n=0) model.

Conclusions:

• The generalized interacting self-avoiding trail model offers a more comprehensive description of polymer-like systems.
• The observed collapse behavior suggests universality under certain conditions, even with added complexity.
• This work advances the understanding of phase transitions and conformational properties in interacting trail systems.