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

Abstract

In a recent paper by Beaton et al, it was 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 $1+\sqrt{2}$. Their proof used a generalisation of an identity obtained by Duminil-Copin and Smirnov, and confirmed a conjecture of Batchelor and Yung. We consider a similar model of self-avoiding walk adsorption on the honeycomb lattice, but with the lattice rotated by $\pi /2$. For this model there also exists a conjecture for the critical surface fugacity, made in 1998 by Batchelor, Bennett-Wood and Owczarek. Using similar methods to Beaton et al, we prove that this is indeed the critical fugacity.

28 pages, 9 figures

References in corpus (2)

• Self-avoiding walk is sub-ballistic
• The critical surface fugacity of self-avoiding walks on a rotated honeycomb lattice

Cited by in corpus (3)

• Discrete holomorphicity and integrability in loop models with open boundaries
• Integrability as a consequence of discrete holomorphicity: the Z_N model
• The critical surface fugacity of self-avoiding walks on a rotated honeycomb lattice