A solvable non-directed model of polymer adsorption

Abstract

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.

18 pages, 6 figures

References in corpus (4)

• A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice
• Calculation of the connective constant for self-avoiding walks via the pivot algorithm
• Pulling adsorbed self-avoiding walks from a surface
• Exact Solution of Semi-Flexible and Super-Flexible Interacting Partially Directed Walks

Cited by in corpus (3)

• Interacting partially directed self-avoiding walk: a probabilistic perspective
• Scaling limit of the uniform prudent walk
• Collapse transition of the interacting prudent walk