CRITICAL-BEHAVIOR OF SELF-AVOIDING WALKS ON FRACTALS

Using a new graph counting technique suitable for self-similar fractal s, exact 18th-order series expansions for SAWs on some Sierpinski carp ets are generated. From them, the critical fugacity x(c) and critical exponents nu(SAW) and gamma(SAW) are obtained. The results show a line ar dependence of the critical fugacity with the average number of bond s per site of the lattices studied. We find for some carpets with low lacunarity that nu(SAW)<0.75, thus violating the relation nu(SAW)(frac tal)>nu(SAW)(d) for SAWs on the fractals which are embedded in a d-dim ensional Euclidean space.