Self-avoiding walks on a bilayer Bethe lattice

Abstract

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