Phase diagram of the interacting partially directed self-avoiding walk attracted by a vertical wall

Elric Angot; Nicolas Pétrélis; Julien Poisat

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arXiv · 2502.03844

Phase diagram of the interacting partially directed self-avoiding walk attracted by a vertical wall

Elric Angot·Nicolas Pétrélis·Julien Poisat

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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.

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Elric Angot, Nicolas Pétrélis, Julien Poisat. 2025-02-06. Phase diagram of the interacting partially directed self-avoiding walk attracted by a vertical wall. https://arxiv.org/abs/2502.03844

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