Critical behaviour of the bond-interacting self-avoiding walk

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.

21 pages and 14 figures. Submited J Phys A

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• The competition of hydrogen-like and isotropic interactions on polymer collapse
• Grand-canonical solution of semi-flexible self-avoiding trails on the Bethe lattice
• Polymer models with competing collapse interactions on Husimi and Bethe lattices
• The statistical mechanics of the two-dimensional hydrogen-bonding self-avoiding walk including solvent effects
• Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares
• A semi-flexible attracting-segment model of three-dimensional polymer collapse
• Bethe approximation for the hydrogen-bonding self-avoiding walk in a solvent
• Self-avoiding walks on a bilayer Bethe lattice
• Semianalytical solutions of Ising-like and Potts-like magnetic polymers on the Bethe lattice