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

• Published in: Journal of physics. Condensed matter Vol. 18; no. 50; pp. 11585 - 11594
• Main Authors: Nicholson, D M C, Barabash, R I, Ice, G E, Sparks, C J, Lee Robertson, J, Wolverton, C
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 20.12.2006; Institute of Physics
• Subjects: Condensed matter: structure, mechanical and thermal properties; Crystalline state (including molecular motions in solids); Exact sciences and technology; Lattice theory and statistics (ising, potts, etc.); Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Structure of solids and liquids; crystallography; Theory of crystal structure, crystal symmetry; calculations and modeling; Many body theory; Fluctuations; Solid solutions; Pair potentials; Hamiltonians; Pair correlation; Density functional method; Ising model; Short-range order; Atomic structure; Classical theory; Thermodynamic equilibrium
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/18/50/013

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.