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arXiv · 1506.06436

A solvable non-directed model of polymer adsorption

Nicholas R. Beaton·Gerasim K. Iliev
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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.

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Nicholas R. Beaton, Gerasim K. Iliev. 2015-06-22. A solvable non-directed model of polymer adsorption. https://doi.org/10.1088/1742-5468%2F2015%2F09%2Fp09014

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