Asymptotic behavior of spanning forests and connected spanning subgraphs on two-dimensional lattices

Shu Chiuan Chang, Robert Shrock

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We calculate exponential growth constants φ and σ describing the asymptotic behavior of spanning forests and connected spanning subgraphs on strip graphs, with arbitrarily great length, of several two-dimensional lattices, including square, triangular, honeycomb, and certain heteropolygonal Archimedean lattices. By studying the limiting values as the strip widths get large, we infer lower and upper bounds on these exponential growth constants for the respective infinite lattices. Since our lower and upper bounds are quite close to each other, we can infer very accurate approximate values for these exponential growth constants, with fractional uncertainties ranging from O(10-4) to O(10-2). We show that φ and σ are monotonically increasing functions of vertex degree for these lattices.

Original languageEnglish
Article number2050249
JournalInternational Journal of Modern Physics B
Volume34
Issue number27
DOIs
Publication statusPublished - 2020 Oct 30

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

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