On the localized phase of a copolymer in an emulsion: subcritical percolation regime

TL;DR

This paper analyzes a two-dimensional directed copolymer model in an emulsion, revealing a complex phase diagram with four phases and multiple critical points in the subcritical percolation regime.

Contribution

It extends previous work by characterizing the phase diagram of the copolymer model in the subcritical regime, identifying four distinct phases and tricritical points.

Findings

Phase diagram has four phases separated by three critical curves.

Identifies two tricritical points where critical curves meet.

Provides a detailed description of phase transitions in the subcritical regime.

Abstract

The present paper is a continuation of \cite{dHP07b}. The object of interest is a two-dimensional model of a directed copolymer, consisting of a random concatenation of hydrophobic and hydrophilic monomers, immersed in an emulsion, consisting of large blocks of oil and water arranged in a percolation-type fashion. The copolymer interacts with the emulsion through an interaction Hamiltonian that favors matches and disfavors mismatches between the monomers and the solvents, in such a way that the interaction with the oil is stronger than with the water. The model has two regimes, supercritical and subcritical, depending on whether the oil blocks percolate or not. In \cite{dHP07b} we focussed on the supercritical regime and obtained a complete description of the phase diagram, which consists of two phases separated by a single critical curve. In the present paper we focus on the subcritical regime and show that the phase diagram consists of four phases separated by three critical curves meeting in two tricritical points.