Critical behaviour of the bond-interacting self-avoiding walk

TL;DR

This paper investigates the phase diagram of the bond-interacting self-avoiding walk, revealing a richer structure than the $ heta$-point model, including a BKT transition line and a critical end point, using transfer matrix methods.

Contribution

It introduces a detailed phase diagram for the model, identifying a BKT transition line and a critical end point, expanding understanding of self-avoiding walk behaviors.

Findings

Discovery of a richer phase diagram than the $ heta$-point model.

Identification of a BKT transition line in the phase diagram.

Contradicts previous transfer matrix results by Machado et al.

Abstract

The phase diagram for the bond-interacting self-avoiding walk is calculated using transfer matrices on finite strips. The model is shown to have a richer phase diagram than the related $\Theta$-point model. In addition to the standard collapse transition, we conjecture the existence of a line of transitions in the Berezinskii--Kosterlitz--Thouless (BKT) universality class, terminating in a critical end point. Our results are in contradiction with a previous transfer matrix calculation by Machado K D, de Oliveira M J and Stilck J F 2001 {\em Phys Rev E} {\bf 64} 051810.