Depinning transition of a directed polymer by a periodic potential: a d-dimensional solution

TL;DR

This paper provides exact formulas for the depinning transition of a directed polymer in a d-dimensional space with a periodic potential, revealing a second-order phase transition and the possibility of localization even with non-attractive average potentials.

Contribution

It offers exact solutions for the critical pinning conditions in all dimensions and analyzes the nature of the phase transition in this model.

Findings

Exact formulas for critical pinning in all dimensions

Depinning transition is of second order

Localization can occur with non-attractive average potentials

Abstract

We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the polymer. We show that a bounded state can still arise even if, in average, the potential layer is not attractive and for diverging values of the potential on the repulsive sites. The phase transition is of second order.