The critical surface fugacity for self-avoiding walks on a rotated honeycomb lattice

Abstract

In a recent paper with Bousquet-Mélou, de Gier, Duminil-Copin and Guttmann (2012), we proved that a model of self-avoiding walks on the honeycomb lattice, interacting with an impenetrable surface, undergoes an adsorption phase transition when the surface fugacity is 1+√2. Our proof used a generalisation of an identity obtained by Duminil-Copin and Smirnov (2012), and confirmed a conjecture of Batchelor and Yung (1995). Here we consider a similar model of self-avoiding walk adsorption on the honeycomb lattice, but with the impenetrable surface placed at a right angle to the previous orientation. For this model there also exists a conjecture for the critical surface fugacity, made by Batchelor, Bennett-Wood and Owczarek (1998). We adapt the methods of the earlier paper to this setting in order to prove the critical surface fugacity, but have to deal with several subtle complications which arise. This article is an abbreviated version of a paper of the same title, currently being prepared for submission.