On the Near-Critical Behavior of Continuous Polymers

TL;DR

This paper studies how the size of a continuous polymer changes near critical temperature conditions when the polymer length becomes very large, revealing complex behaviors in such near-critical regimes.

Contribution

It provides a detailed analysis of the joint effects of temperature approaching criticality and infinite polymer length on polymer size distribution.

Findings

Polymer size exhibits critical scaling behavior near the transition.

The interplay of temperature and chain length leads to intricate size distribution patterns.

Results enhance understanding of phase transitions in polymer systems.

Abstract

The aim of this paper is to investigate the distribution of a continuous polymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously and independently vary two parameters: the temperature, which approaches the critical value, and the length of the polymer chain, which tends to infinity. We describe how the typical size of the polymer depends on the two parameters.