Journal article

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

NR Beaton

Journal of Physics A Mathematical and Theoretical | IOP PUBLISHING LTD | Published : 2014

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 . Their proof used a generalization 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 π/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 critic..

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University of Melbourne Researchers

Grants

Awarded by National Science Foundation


Funding Acknowledgements

I thank Murray Batchelor for suggesting this problem, and Tony Guttmann and Mireille Bousquet-Melou for helpful conversations. I received support from the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS), as well as the Australian Mathematical Society (AustMS) in the form of a Lift-Off Fellowship. Part of this work was carried out while I was a guest of the Mathematical Sciences Research Institute (MSRI) in Berkeley, CA, during the Spring 2012 Random Spatial Processes Program, and I thank the Institute for its hospitality and the NSF (grant DMS-0932078) for its financial support.