Two-dimensional self-avoiding walks and polymer adsorption: critical fugacity estimates
Nicholas R Beaton, Anthony J Guttmann, Iwan Jensen
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2012
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 t..View full abstract
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AJG and IJ acknowledge financial support from the Australian Research Council. NRB was supported by the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS). This work was supported by an award under the Merit Allocation Scheme on the NCI National Facility at the ANU.