Two-dimensional self-avoiding walks and polymer adsorption: critical fugacity estimates

Nicholas R. Beaton, Anthony J. Guttmann, Iwan Jensen

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks (SAW) interacting with (alternate) sites on the surface of the honeycomb lattice is 1+ √2.Akey identity used in that proof depends on the existence of a parafermionic observable for SAW interacting with a surface on the honeycomb lattice. Despite the absence of a corresponding observable for SAWon the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed for the honeycomb lattice persist irrespective of lattice. This permits the accurate estimation of the critical fugacity for the corresponding problem for the square and triangular lattices.We consider both edge and site weighting, and results of unprecedented precision are achieved. We also prove the corresponding result for the edge-weighted case for the honeycomb lattice.

Original languageEnglish
Article number055208
JournalJournal of Physics A: Mathematical and Theoretical
Issue number5
Publication statusPublished - 16 Jan 2012
Externally publishedYes


Dive into the research topics of 'Two-dimensional self-avoiding walks and polymer adsorption: critical fugacity estimates'. Together they form a unique fingerprint.

Cite this