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arXiv:cond-mat/0609091 · Journal of Physics A Mathematical and Theoretical

Critical behaviour of the bond-interacting self-avoiding walk

Damien Paul Foster

Published Feb 14, 2007• 17 citations
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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.

DOI
10.1088/1751-8113/40/9/004

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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 Θ\ThetaΘ-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.
The phase diagram and surface critical behaviour of the vertex-interacting self-avoiding walk are examined using transfer matrix methods extended using DMRG and coupled with finite-size scaling. Particular attention is paid to the critical exponents at the ordinary and special points along the collapse transition line. The question of the bulk exponents (ννν and γγγ) is addressed, and the results found are at variance with previously conjectured exact values.
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