IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v128y1984i1p334-350.html
   My bibliography  Save this article

Generalized cluster description of multicomponent systems

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437184900967
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/0378-4371(84)90096-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Guerrero, Alejandra I., 2023. "Magnetocaloric effect in the Jx−Jy Blume–Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    4. 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.
    5. 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.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bondarev, B.V., 1989. "Binary alloys. Statistical theory of non-equilibrium states. Kinetics of ordering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 155(1), pages 123-166.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:128:y:1984:i:1:p:334-350. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.