Generalised interacting self-avoiding trails on the square lattice: phase diagram and critical behaviour

TL;DR

This paper introduces a generalized interacting self-avoiding trail model on the square lattice, incorporating crossings, collisions, and rigidity, and analyzes its phase diagram and critical behavior using numerical transfer matrix methods.

Contribution

It extends existing models by including crossings and rigidity, unifying several models and analyzing their collapse behavior and phase transitions.

Findings

Collapse behavior matches that of the pure interacting self-avoiding trail model

Model includes special cases like the Nienhuis O(n=0) model

Phase diagram and critical behavior characterized numerically

Abstract

A generalised model for interacting self-avoiding trails on the square lattice is presented and studied using numerical transfer matrix methods. The model differentiates between on-site double visits corresponding to collisions, and crossings. Rigidity is also included in the model. The model includes the Nienhuis O(n=0) model and the interacting self-avoiding trail model as special cases. It is shown that the generic type of collapse found is the same as the pure interacting self-avoiding trail model.