DIRECTED SELF-AVOIDING WALKS ON SIERPINSKI CARPETS - SERIES RESULTS

Using a graph counting technique suitable for self-similar fractals we obtain the exact densities of partially (PDSAW) and fully (FDSAW) dir ected self-avoiding walks on Sierpinski carpets. From them we calculat e the root-mean-square transverse and longitudinal displacements of th e n-step walks up to n = 20 for PDSAWS and up to n = 23 for FDSAWS. Th e critical exponents nu(perpendicular to) found for the PDSAW depend o n the fractal dimension as well as on the lacunarity of the lattice. T he results indicate that PDSAWS and FDSAWS have different critical beh aviour on the same carpet.