2020/07/22 by Alexandre Legrand, Legrand, Alexandre, Nicolas Pétrélis +1
Materials Science · Mathematics · Physics and Astronomy · #60K35 #82B41 #FOS: Mathematics #Material Dynamics and Properties #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2007.11313
openalex publication_date 2020/07/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The present paper is dedicated to the 2-dimensional Interacting Partially Directed Self Avoiding Walk constrained to remain in the upper-half plan and interacting with the horizontal axis. The model has been introduced in \citeF90 to investigate the behavior of a homopolymer dipped in a poor solvent and adsorbed along a horizontal hard wall. It is known to undergo a collapse transition between an extended phase, inside which typical configurations of the polymer have a large horizontal extension (comparable to their total size), and a collapsed phase inside which the polymer looks like a globule. In the present paper, we establish rigorously that inside the collapsed phase, a surface transition occurs between an adsorbed-collapsed regime where the bottommost layer of the globule is pinned at the hard wall, and a desorbed-collapsed regime where the globule wanders away from the wall. To prove the existence of this surface transition and exhibit its associated critical curve, we display some sharp asymptotics of the partition function for a slightly simplified version of the model.