Unbinding of mutually avoiding random walks and two dimensional quantum gravity

TL;DR

This paper investigates the unbinding transition of mutually avoiding random walks on a 2D lattice polymer, revealing a strong first-order phase transition and employing conformal mapping techniques related to quantum gravity for analysis.

Contribution

It introduces an exact analytical approach using conformal mapping to quantum gravity for analyzing unbinding transitions in 2D polymers with mutually avoiding walks.

Findings

Unbinding transition is strongly first order.

Entropic exponents show sharp changes at the transition.

Analytical and numerical results are in excellent agreement.

Abstract

We analyze the unbinding transition for a two dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that unbinding in this model is a strong first order transition. The entropic exponents associated to denaturated loops and end-segments distributions show sharp differences at the transition point and in the high temperature phase. Their values can be deduced from some exact arguments relying on a conformal mapping of copolymer networks into a fluctuating geometry, i.e. in the presence of quantum gravity. An excellent agreement between analytical and numerical estimates is observed for all cases analized.