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

A generalized model for interacting self-avoiding trails on a 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 in the pure interacting self-avoiding trail model.