Painleve III and 2D Polymers

TL;DR

This paper explores the connection between Painleve III transcendents and the scaling functions of 2D polymers, extending previous results to contractible loops through analytical and numerical methods.

Contribution

It establishes a new relation between Painleve III and the thermodynamic properties of contractible 2D polymer loops using perturbation theory and Bethe ansatz.

Findings

Relation between Painleve III and contractible loops confirmed

Analytical and numerical methods support the new connection

Extends previous work on non-contractible loops

Abstract

Recently the scaling function of the dilute non-contractible self-avoiding 2D polymer loop on a cylinder was related to the Painleve III transcendent. Using the perturbation theory, the thermidynamic Bethe ansatz and numerical calculations we argue a similar relation for the contractible self-avoiding loop.