Crossover exponent for piecewise directed walk adsorption on Sierpinski fractals

Abstract

We study the problem of critical adsorption of piecewise directed random walks on a boundary of fractal lattices that belong to the Sierpinski gasket family. By applying the exact real space renormalization group method, we calculate the crossover exponent φ, associated with the number of adsorbed steps, for the complete fractal family. We demonstrate that our results are very close to the results obtained for ordinary self-avoiding walk, and discuss the asymptotic behaviour of φ at the fractal to Euclidean lattice crossover.