Relationship between pair and higher-order correlations in solid solutions and other Ising systems

D. M C Nicholson, R. I. Barabash, G. E. Ice, C. J. Sparks, J. Lee Robertson, C. Wolverton

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Atomic structure is perhaps the information most critical to the understanding of materials behaviour, hence the great importance of x-rays and neutrons as probes. Although scattering is sensitive to pair and higher-order correlations, in most applications only the pair correlation is recovered. However, pair correlation is inadequate for a complete description of homogeneous systems in thermodynamic equilibrium; all correlations are required. It is often assumed that the pair correlations extracted from scattering experiments either uniquely determine or greatly restrict higher-order correlations. Here we argue on the basis of simulations and classical density functional theory that when the Hamiltonian is of pair-potential form the pair correlations do uniquely determine all higher-order correlations. However, we also demonstrate by simulation and prove algebraically that for specific many-body Hamiltonians additional information beyond pair correlations is needed to determine higher-order correlations. The derivations are underpinned by the close connection between fluctuations, applied fields, and correlations and identify approaches that hold promise for extracting higher-order correlations.

Original languageEnglish (US)
Article number013
Pages (from-to)11585-11594
Number of pages10
JournalJournal of Physics Condensed Matter
Issue number50
StatePublished - Dec 20 2006

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics


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