Trapping statistics in growing self-interacting self-avoiding walks: Square versus honeycomb lattices

Area of Science:

• Statistical Physics
• Computational Physics
• Polymer Physics

Background:

• Growing self-avoiding walks (GSAW) are a fundamental model in statistical physics.
• Understanding GSAW universality classes is crucial for theoretical advancements.
• Existing research primarily focuses on equally weighted self-avoiding walks.

Purpose of the Study:

• To expand the understanding of growing self-interacting self-avoiding walks (GSISAW).
• To investigate the interplay between lattice geometry and interaction strength in GSISAW.
• To analyze the trapping effect in GSISAW models by examining decision points.

Main Methods:

• Numerical simulations of GSISAW on square and honeycomb lattices.
• Comparative analysis of walk behavior across different lattice structures.
• Enhanced analysis of decision points to understand trapping mechanisms.

Main Results:

• A minimum in mean trapping length was observed as interaction strength varied on the honeycomb lattice.
• Similar trapping behavior was noted on square lattices, indicating a general trend.
• Saturation effects in mean trapping lengths and insights from trap size were identified.

Conclusions:

• Lattice geometry and interaction strength significantly influence GSISAW behavior.
• The trapping effect is a key characteristic, with predictable patterns across lattices.
• This study provides a deeper understanding of GSISAW, contributing to statistical physics models.