On the number of contacts of two polymer chains situated on fractal structures

We study the critical behavior of the number of monomer-monomer contacts for two polymers in a good solvent. Polymers are modeled by two self-avoiding walks situated on fractals that belong to the checkerboard (CB) and X family. Each member of a family is labeled by an odd integer b, <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$3\le b\le\infty$</EquationSource> </InlineEquation>. By applying the exact Renormalization Group (RG) method, we establish the relevant phase diagrams whereby we calculate the contact critical exponents <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\varphi$</EquationSource> </InlineEquation> (for the CB and X fractals with b=5 and b=7). The critical exponent <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\varphi$</EquationSource> </InlineEquation> is associated with power law of the number of sites at which the two polymers are touching each other. Copyright Springer-Verlag Berlin/Heidelberg 2004