  We study the polymer system consisting of two polymer chains situated in a
fractal container that belongs to the three--dimensional Sierpinski Gasket (3D
SG) family of fractals. Each 3D SG fractal has four fractal impenetrable 2D
surfaces, which are, in fact, 2D SG fractals. The two-polymer system is
modelled by two interacting self-avoiding walks (SAWs), one of them
representing a 3D floating polymer, while the other corresponds to a chain
adhered to one of the four 2D SG boundaries. We assume that the studied system
is immersed in a poor solvent inducing the intra-chain interactions. For the
inter-chain interactions we propose two models: in the first model (ASAWs) the
SAW chains are mutually avoiding, whereas in the second model (CSAWs) chains
can cross each other. By applying an exact Renormalization Group (RG) method,
we establish the relevant phase diagrams for $b=2,3$ and $b=4$ members of the
3D SG fractal family for the model with avoiding SAWs, and for $b=2$ and $b=3$
fractals for the model with crossing SAWs. Also, at the appropriate transition
fixed points we calculate the contact critical exponents, associated with the
number of contacts between monomers of different chains. Throughout the paper
we compare results obtained for the two models and discuss the impact of the
topology of the underlying lattices on emerging phase diagrams.

Statistical Mechanics