Critical adsorption of random walks on fractal lattices with uniform coordination number

We study the problem of adsorption of random walks on a boundary of fractal lattices that have uniform coordination numbers. More specifically, for a suitable Gaussian model, situated on the Sierpiński gasket fractals with an interacting wall, we analyze critical properties using the renormalization group approach. In this way we have found exact expressions for a set of pertinent critical exponents. In particular, we have demonstrated that the crossover critical exponent, associated with the number of adsorbed monomers, can be expressed as simple combination of only three quantities—the end-to-end distance critical exponent, the substratum fractal dimension, and the adsorbing boundary fractal dimension.