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Generalized cluster description of multicomponent systems

Author

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  • Sanchez, J.M.
  • Ducastelle, F.
  • Gratias, D.

Abstract

A general formalism for the description of configurational cluster functions in multicomponent systems is developed. The approach is based on the description of configurational cluster functions in terms of an orthogonal basis in the multidimensional space of discrete spin variables. The formalism is used to characterize the reduced density matrices (or cluster probability densities) and the free energy functional obtained in the Cluster Variation Method approximation. For the particular representation chosen, the expectation values of the base functions are the commonly used multisite correlation functions. The latter form an independent set of variational parameters for the free energy which, in general, facilitates the minimization procedure. A new interpretation of the Cluster Variation Method as a self-consistency relation on the renormalized cluster energies is also presented.

Suggested Citation

  • Sanchez, J.M. & Ducastelle, F. & Gratias, D., 1984. "Generalized cluster description of multicomponent systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 334-350.
    • Handle: RePEc:eee:phsmap:v:128:y:1984:i:1:p:334-350
    DOI: 10.1016/0378-4371(84)90096-7
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    References listed on IDEAS

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    1. Gratias, D. & Sanchez, J.M. & De Fontaine, D., 1982. "Application of group theory to the calculation of the configurational entropy in the cluster variation method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(1), pages 315-337.
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    Cited by:

    1. Sluitter, M. & Turchi, P. & Zezhong, Fu & De Fontaine, D., 1988. "Re-examination of BCC based phase diagrams with constant first and second neighbor pair interactions in the cluster variation approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 148(1), pages 61-73.
    2. Guerrero, Alejandra I. & Stariolo, Daniel A., 2017. "Pair correlations and structure factor of the J1-J2 square lattice Ising model in an external field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 596-606.
    3. Ceder, G. & Dreyssé, H. & de Fontaine, D., 1993. "Triplet interactions and the c(2×2) overlayer phase diagram," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 193(1), pages 105-113.
    4. Linze Li & Bin Ouyang & Zhengyan Lun & Haoyan Huo & Dongchang Chen & Yuan Yue & Colin Ophus & Wei Tong & Guoying Chen & Gerbrand Ceder & Chongmin Wang, 2023. "Atomic-scale probing of short-range order and its impact on electrochemical properties in cation-disordered oxide cathodes," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    5. Van der Ven, A. & Thomas, J.C. & Xu, Qingchuan & Bhattacharya, J., 2010. "Linking the electronic structure of solids to their thermodynamic and kinetic properties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(7), pages 1393-1410.
    6. Guerrero, Alejandra I., 2023. "Magnetocaloric effect in the Jx−Jy Blume–Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).

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