Enumerations of lattice animals and trees

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

We have developed an improved algorithm that allows us to enumerate the number of site animals on the square lattice up to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyration of both lattice animals and trees up to size 42. Analysis of the resulting series yields an improved estimate, λ = 4.062570(8), for the growth constant of lattice animals, and, λ0 = 3.795254(8), for the growth constant of trees, and confirms to a very high degree of certainty that both the animal and tree generating functions have a logarithmic divergence. Analysis of the radius of gyration series yields the estimate, v = 0.64115(5), for the size exponent.

Original languageEnglish
Pages (from-to)865-881
Number of pages17
JournalJournal of Statistical Physics
Volume102
Issue number3-4
DOIs
Publication statusPublished - Feb 2001
Externally publishedYes

Keywords

  • Computer algorithms
  • Exact enumeration
  • Lattice animals

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