Hamiltonian walks on Sierpinski and n-simplex fractals

Abstract

We study Hamiltonian walks (HWs) on Sierpinski and n-simplex fractals. Via numerical analysis of exact recursion relations for the number of HWs we calculate the connectivity constant ω and find the asymptotic behaviour of the number of HWs. Depending on whether or not the polymer collapse transition is possible on a studied lattice, different scaling relations for the number of HWs are obtained. These relations are, in general, different from the well-known form characteristic of homogeneous lattices which has thus far been assumed to also hold for fractal lattices. © 2005 IOP Publishing Ltd.