The critical exponents ν, ν||and ν⊥of directed SAW on Sierpinski carpets: a computer simulation study

The critical behaviour of fully directed self-avoiding walks (DSAW) on Sierpinski carpets is studied by numerical simulation. The authors propose a fractal cell generation method to form an infinite fractal lattice with the structure of a Sierpinski carpet. The obtained critical exponent ν || is independent of the fractal dimension of a Sierpinski carpet d f but ν and ν ⊥ are dependent on d f . The results indicate that DSAW on different Sierpinski carpets belong to different universality classes.