Self-avoiding walks on a bilayer Bethe lattice

TL;DR

This paper models polymer chains confined to a bilayer structure using a bilayer Bethe lattice, revealing a complex phase diagram with multiple critical and multicritical points.

Contribution

It introduces a novel bilayer Bethe lattice model for polymers, analyzing its thermodynamic properties and complex phase behavior.

Findings

Rich phase diagram with critical, coexistence, tricritical, bicritical, and multicritical points.

Identification of various phase transition lines and multicritical points.

Analysis of interlayer interactions affecting polymer configurations.

Abstract

We propose and study a model of polymer chains in a bilayer. Each chain is confined in one of the layers and polymer bonds on first neighbor edges in different layers interact. We also define and comment results for a model with interactions between monomers on first neighbor sites of different layers. The thermodynamic properties of the model are studied in the grand-canonical formalism and both layers are considered to be Cayley trees. In the core region of the trees, which we may call a bilayer Bethe lattice, we find a very rich phase diagram in the parameter space defined by the two activities of monomers and the Boltzmann factor associated to the interlayer interaction between bonds or monomers. Beside critical and coexistence surfaces, there are tricritical, bicritical and critical endpoint lines, as well as higher order multicritical points.