Statistical mechanics of two-dimensional tilings

F.H. Kaatz, Ernesto Estrada, A. Bultheel, N. Sharrock

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Reduced dimensionality in two dimensions is a topic of current interest. We use model systems to investigate the statistical mechanics of ideal networks. The tilings have possible applications such as the 2D locations of pore sites in nanoporous arrays (quantum dots), in the 2D hexagonal structure of graphene, and as adsorbates on quasicrystalline crystal surfaces. We calculate the statistical mechanics of these networks, such as the partition function, free energy, entropy, and enthalpy. The plots of these functions versus the number of links in the finite networks result in power law regression. We also determine the degree distribution, which is a combination of power law and rational function behavior. In the large-scale limit, the degree of these 2D networks approaches 3, 4, and 6, in agreement with the degree of the regular tilings. In comparison, a Penrose tiling has a degree also equal to about 4.
Original languageEnglish
Pages (from-to)2957-2963
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume391
Issue number10
Early online date12 Jan 2012
DOIs
Publication statusPublished - 15 May 2012

Keywords

  • regular tilings
  • degree distribution
  • power laws
  • finite graph
  • statistical mechanics functions
  • Penrose tiling

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