Exponential Growth Constants for Spanning Forests on Archimedean Lattices: Values and Comparisons of Upper Bounds

2020/12/25 by Shu-Chiuan Chang, Robert Shrock
Mathematics · Physics and Astronomy · #cond-mat.stat-mech #math.CO

paper · pdf · doi:10.1142/s0217979221500855

published as IJMPB (Internat. J. Mod. Phys. B) 35, 2150085 (2021) · 5 pages, latex. arXiv admin note: text overlap with arXiv:2002.07150, arXiv:1810.07357

arxiv created 2020/12/25 · arxiv updated 2021/04/12

Abstract

We compare our upper bounds on the exponential growth constant ϕ(Λ) characterizing the asymptotic behavior of spanning forests on Archimedean lattices Λ with recently derived upper bounds. Our upper bounds on ϕ(Λ), which are very close to the respective values of ϕ(Λ) that we have calculated, are shown to be significantly better for these lattices than the new upper bounds.

Citations

• Asymptotic behavior of spanning forests and connected spanning subgraphs on two-dimensional lattices
• Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs