Continuous melting of compact polymers

TL;DR

This paper provides exact results for a two-dimensional lattice model of compact polymers, revealing a continuous melting transition between disordered and crystalline phases, with precise critical exponents.

Contribution

It offers the first exact analysis of the order-disorder transition in the Flory model for 2D compact polymers, clarifying the nature of the transition.

Findings

Identifies a continuous melting transition in the 2D Flory model

Calculates exact critical exponents at the transition point

Relevance for polymers on surfaces like DNA on lipid bilayers

Abstract

The competition between chain entropy and bending rigidity in compact polymers can be addressed within a lattice model introduced by P.J. Flory in 1956. It exhibits a transition between an entropy dominated disordered phase and an energetically favored crystalline phase. The nature of this order-disorder transition has been debated ever since the introduction of the model. Here we present exact results for the Flory model in two dimensions relevant for polymers on surfaces, such as DNA adsorbed on a lipid bilayer. We predict a continuous melting transition, and compute exact values of critical exponents at the transition point.