Correlated cluster mean-field theory for spin systems

Daisuke Yamamoto*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Citations (Scopus)


A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. We divide the lattice sites into clusters whose size and shape are selected so that the equivalence of all sites in a cluster is preserved. Since the strength of interactions of a cluster with its surrounding clusters is strongly dependent on the spin configuration of the central cluster itself, we include this contribution in the effective fields acting on the spins. The effects of "correlations" between clusters can be taken into account beyond the standard mean-field level and as a result our cluster-based method gives qualitatively (and even quantitatively) correct results for the both Ising and Heisenberg models. Especially, for the Ising model on the honeycomb and square lattices, the calculated results of the critical temperature are very close (overestimated by only less than 5%) to the exact values.

Original languageEnglish
Article number144427
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number14
Publication statusPublished - 2009 Apr 1

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials


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