Duality mapping and unbinding transitions of semiflexible and directed polymers

TL;DR

This paper establishes a duality mapping between directed and semiflexible polymers, enabling exact determination of critical exponents, transition points, and order for their unbinding transitions under short-range attraction.

Contribution

It introduces a duality mapping that relates the unbinding behavior of filaments and strings, providing exact results for critical properties.

Findings

Exact critical exponents for unbinding transitions

Precise transition points identified

Determination of transition order

Abstract

Directed polymers (strings) and semiflexible polymers (filaments) are one-dimensional objects governed by tension and bending energy, respectively. They undergo unbinding transitions in the presence of a short-range attractive potential. Using transfer matrix methods we establish a duality mapping for filaments and strings between the restricted partition sums in the absence and the presence of a short-range attraction. This allows us to obtain exact results for the critical exponents related to the unbinding transition, the transition point and transition order.