Nature of the collapse transition in interacting self-avoiding trails

Area of Science:

• Statistical Mechanics
• Polymer Physics
• Phase Transitions

Background:

• The interacting self-avoiding trail (ISAT) model is crucial for understanding polymer behavior.
• Previous studies on lattices have shown varied phase diagrams and transition behaviors.

Purpose of the Study:

• To investigate the phase diagrams of the ISAT model on Bethe and Husimi lattices.
• To analyze the effects of monomer capacity (K) and site-visit weights (ωᵢ) on phase transitions.
• To compare ISAT behavior with interacting self-avoiding walks and explain observed differences in collapse transitions.

Main Methods:

• Exact grand-canonical solutions were derived for the ISAT model.
• The study considered lattices with general coordination (q) and specific square lattices (q=4).
• Monomer capacity (K) and site-visit weights (ωᵢ) were incorporated into the model.

Main Results:

• Rich phase diagrams were found, featuring nonpolymerized, regular polymerized, and dense polymerized phases.
• Transitions were characterized as continuous and discontinuous, with complex structures for higher q and K values.
• For q=4, K=2, the collapse transition was identified as a bicritical point, with the collapsed phase being solidlike.

Conclusions:

• The ISAT model exhibits complex phase behavior on Bethe and Husimi lattices, influenced by lattice coordination and monomer capacity.
• The findings provide a potential explanation for differences in collapse transitions between ISATs and self-avoiding walks.
• The study maps phase diagrams to the canonical ensemble, facilitating comparison with simulation results on regular lattices.