Hamiltonian walks on Sierpinski and n-simplex fractals

Details Hamiltonian walks on Sierpinski and n-simplex fractals Hamiltonian walks on Sierpinski and n-simplex fractals

2003-10-31

arxiv.org/abs/cond-mat/0310777v3

J. Phys. A: Math. Gen. 38 (2005) 5677-5695

Physics

Condensed Matter

Statistical Mechanics

22 pages, 6 figures; final version

Scientific paper

10.1088/0305-4470/38/25/006

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 $\omega$ 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 hold for fractal lattices too.

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