Hamiltonian walks on Sierpinski and n-simplex fractals

TL;DR

This paper investigates Hamiltonian walks on Sierpinski and n-simplex fractals, analyzing their enumeration and asymptotic behavior, revealing different scaling relations depending on the polymer collapse transition.

Contribution

It provides the first detailed numerical analysis of HWs on these fractals, deriving new scaling relations that differ from those on homogeneous lattices.

Findings

Calculated the connectivity constant ω for HWs on fractals.

Identified different scaling relations based on collapse transition possibilities.

Showed that fractal lattices exhibit unique HW scaling behaviors.

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 $\omega$ 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.