Two-sided prudent walks: a solvable non-directed model of polymer adsorption
Nicholas R Beaton, Gerasim K Iliev
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | IOP PUBLISHING LTD | Published : 2015
Prudent walks are self-avoiding walks which cannot step towards an already occupied vertex. We introduce a new model of adsorbing prudent walks on the square lattice, which start on an impenetrable surface and accrue a fugacity a with each step along the surface. These are different to other exactly solved models of polymer adsorption, like Dyck paths, Motzkin paths and partially-directed walks, in that they are not trivially directed-they are able to step in all lattice directions. We calculate the generating functions, free energies and surface densities for this model and observe a first-order adsorption transition at the critical value of the surface interaction.
The authors thank S Whittington and T Guttmann for helpful conversations. Parts of this work were conducted while both authors received support from the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS). NRB is supported by the PIMS Collaborative Research Group in Applied Combinatorics.