Random copolymer: Gaussian variational approach

TL;DR

This paper develops a Gaussian variational mean field theory to analyze phase transitions in a quenched disordered random copolymer, revealing scale-dependent freezing and topological frustration.

Contribution

It introduces a replica variational approach to study collapse, phase separation, and freezing transitions in a single framework for random copolymers.

Findings

Derived an analytical free energy expression.

Identified a scale-dependent freezing transition.

Mapped the phase diagram showing topological frustration.

Abstract

We study the phase transitions of a random copolymer chain with quenched disorder. We apply a replica variational approach based on a Gaussian trial Hamiltonian in terms of the correlation functions of monomer Fourier coordinates. This allows us to study collapse, phase separation and freezing transitions within the same mean field theory. The effective free energy of the system is derived analytically and analysed numerically. Such quantities as the radius of gyration or the average value of the overlap between different replicas are treated as observables and evaluated by introducing appropriate external fields to the Hamiltonian. We obtain the phase diagram and show that this system exhibits a scale dependent freezing transition. The correlations between replicas appear at different length scales as the temperature decreases. This indicates the existence of the topological frustration.