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

Fuente: arXiv
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Autores principales: Angot, Elric, Pétrélis, Nicolas, Poisat, Julien
Formato: Preprint
Publicado: 2025
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author Angot, Elric
Pétrélis, Nicolas
Poisat, Julien
author_facet Angot, Elric
Pétrélis, Nicolas
Poisat, Julien
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2502_03844
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Phase diagram of the interacting partially directed self-avoiding walk attracted by a vertical wall
Angot, Elric
Pétrélis, Nicolas
Poisat, Julien
Probability
Statistical Mechanics
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.
title Phase diagram of the interacting partially directed self-avoiding walk attracted by a vertical wall
topic Probability
Statistical Mechanics
url https://arxiv.org/abs/2502.03844