Self-avoiding walks on a bilayer Bethe lattice
  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. 
Pablo Serra and J\"urgen F. Stilck
cond-mat.stat-mech cond-mat.soft