A massively parallel supercamputer was nsed to exhaustively enumerate all of the Hamiltonian walks for simple cubic sublattices of four different sizes (up to 3 × 4 × 4). The behaviour of the logarithm of the number of walks was found to be linear in the number of vertices in the lattice. The linear fit is shown to agree also with the asymptotic limit of the Flory mean field theoretical estimate Thus, we suggest that the fit obtained yields the number of walks for any size fragment of the cubic Imice to logarithmic accuracy. The significance of this result to the validily of polymer models is also discussed.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics