Crossover exponent for piecewise directed walk adsorption on Sierpinski fractals

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

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19 pages, 10 figures, Latex2.09 using ioplppt.sty

Scientific paper

10.1088/0305-4470/32/8/004

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

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