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

Abstract

Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks interacting with (alternate) sites on the surface of the honeycomb lattice is $1+\sqrt{2}$. A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks interacting with a surface on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on 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 \emph{prove} the corresponding result fo the edge-weighted case for the honeycomb lattice.

12 pages, 3 figures, 7 tables

References in corpus (2)

• The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is $1+\sqrt{2}$
• A numerical adaptation of SAW identities from the honeycomb to other 2D lattices

Cited by in corpus (7)

• The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is $1+\sqrt{2}$
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• Self-avoiding walks and connective constants in clustered scale-free networks
• Square lattice self-avoiding walks and biased differential approximants
• Microcanonical Simulations of Adsorbing Self-Avoiding Walks
• Partition and generating function zeros in adsorbing self-avoiding walks
• Supermultiplicative relations in models of interacting self-avoiding walks and polygons