Force--induced depinning of directed polymers

TL;DR

This paper investigates how directed polymers interact with a defect line under an external force, revealing inhomogeneous interactions can cause re-entrant phase transitions, with formulas relating free energies and methods to detect these phenomena.

Contribution

It introduces a formula linking free energies of directed polymers with and without force, and demonstrates how inhomogeneous interactions can induce re-entrant transitions.

Findings

Inhomogeneous interactions can cause re-entrant phase transitions.

A formula relates free energy with force to free energy without force.

Detection methods for re-entrant transitions are proposed.

Abstract

We present an approach to studying directed polymers in interaction with a defect line and subject to a force, which pulls them away from the line. We consider in particular the case of inhomogeneous interactions. We first give a formula relating the free energy of these models to the free energy of the corresponding ones in which the force is switched off. We then show how to detect the presence of a re-entrant transition without fully solving the model. We discuss some models in detail and show that inhomogeneous interaction, e.g. disordered interactions, may induce the re-entrance phenomenon.