Critical behavior of the system of two crossing self-avoiding walks on a family of three-dimensional fractal lattices

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. The two-polymer system is modeled by two interacting self-avoiding walks (SAW) immersed in a good solvent. To conceive the inter-chain interactions we apply the model of two crossing self-avoiding walks (CSAW) in which the chains can cross each other. By applying renormalization group (RG) method, we establish the relevant phase diagrams for b=2 and b=3 members of the 3D SG fractal family. Also, at the appropriate transition fixed points we calculate the contact critical exponents φ, associated with the number of contacts between monomers of different chains. For larger b (2⩽b⩽30) we apply Monte Carlo renormalization group (MCRG) method, and compare the obtained results for φ with phenomenological proposals for the contact critical exponent, as well as with results obtained for other similar models of two-polymer system.