Phase diagram of the interacting partially directed self-avoiding walk attracted by a vertical wall
Abstract
In the present paper, we consider the interacting partially-directed self-avoiding walk (IPDSAW) attracted by a vertical wall. The IPDSAW was introduced by Zwanzig and Lauritzen (J. Chem. Phys., 1968) as a manner of investigating the collapse transition of a homopolymer dipped in a repulsive solvent. We prove in particular that a surface transition occurs inside the collapsed phase between (i) a regime where the attractive vertical wall does not influence the geometry of the polymer and (ii) a regime where the polymer is partially attached at the wall on a length that is comparable to its horizontal extension, modifying its asymptotic Wulff shape. The latter rigorously confirms the conjecture exposed by physicists in (Physica A: Stat. Mech. \\& App., 2002). We push the analysis even further by providing sharp asymptotics of the partition function inside the collapsed phase.
Keywords
Cite
@article{arxiv.2502.03844,
title = {Phase diagram of the interacting partially directed self-avoiding walk attracted by a vertical wall},
author = {Elric Angot and Nicolas Pétrélis and Julien Poisat},
journal= {arXiv preprint arXiv:2502.03844},
year = {2025}
}