Collapse transition of the interacting prudent walk
Nicolas P\'etr\'elis, Niccolo Torri

TL;DR
This paper proves the existence of a collapse transition in the 2D interacting prudent walk model, computes its free energy, and compares it with related models, providing new insights into self-avoiding walk behaviors.
Contribution
It demonstrates the collapse transition for a non-directed self-avoiding walk model and relates the free energy of prudent walks to a restricted version, solving open problems.
Findings
IPSAW undergoes a finite-temperature collapse transition.
The free energy of IPSAW equals that of two-sided prudent walks.
The free energy of ISAW exceeds the interaction parameter for all positive beta.
Abstract
This article is dedicated to the study of the 2-dimensional interacting prudent self-avoiding walk (referred to by the acronym IPSAW) and in particular to its collapse transition. The interaction intensity is denoted by and the set of trajectories consists of those self-avoiding paths respecting the prudent condition, which means that they do not take a step towards a previously visited lattice site. The IPSAW interpolates between the interacting partially directed self-avoiding walk (IPDSAW) that was analyzed in details in, e.g., [Zwanzig and Lauritzen, 1968], [Brak et al., 1992], [Carmona, Nguyen and P\'etr\'elis, 2013-2016], and the interacting self-avoiding walk (ISAW) for which the collapse transition was conjectured in [Saleur, 1986]. Three main theorems are proven. We show first that IPSAW undergoes a collapse transition at finite temperature and, up to our knowledge,…
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Advanced Thermodynamics and Statistical Mechanics
