Critical behavior of random polymers

TL;DR

This paper studies the critical behavior of random polymers with attractive potentials, analyzing how their distribution changes as temperature approaches a critical point and polymer length grows infinitely, revealing limiting distributions based on parameter relations.

Contribution

It identifies the limiting distributions of homopolymers near critical temperature as polymer length tends to infinity, considering the interplay of two key parameters.

Findings

Distributions depend on the relation between temperature and polymer length.

Limiting behaviors are characterized after diffusive scaling.

Results reveal phase transition phenomena in polymer models.

Abstract

The aim of this paper is to investigate the distribution of a continuous homopolymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously vary two parameters: the temperature, which approaches the critical value, and the length of the polymer, which tends to infinity. As the main result, we identify the distributions that appear in the limit (after a diffusive scaling of the original polymer measures) and depend on the relation between the two parameters.