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 $\varphi$, 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 $\varphi$ at the fractal to Euclidean lattice crossover.

arXiv comment19 pages, 10 figures, Latex2.09 using ioplppt.sty

References in corpus (1)

• Critical exponents of surface-interacting self-avoiding walks on a family of truncated n-simplex lattices