IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v105y1981i3p620-630.html
   My bibliography  Save this article

Variational principle for regular and random Ising models on the cactus tree or on the usual lattice in the “cactus approximation”

Author

Listed:
  • Morita, T.

Abstract

The distribution functions and the free energy are expressed in terms of the effective fields for the regular and random Ising models of an arbitrary spin S on the generalized cactus tree. The same expressions apply to systems on the usual lattice in the “cactus approximation” in the cluster variation method. For an ensemble of random Ising models of an arbitrary spin S on the generalized cactus tree, the equation for the probability distribution function of the effective fields is set up and the averaged free energy is expressed in terms of the probability distribution. The same expressions apply to the system on the usual lattice in the “cactus approximation”. We discuss the quantities on the usual lattice when the system or the ensemble of random systems has the translational symmetry. Variational properties of the free energy for a system and of the averaged free energy for an ensemble of random systems are noted. The “cactus approximations” are applicable to the Heisenberg model as well as to the Ising model of an arbitrary spin, and to ensembles of random systems of these models.

Suggested Citation

  • Morita, T., 1981. "Variational principle for regular and random Ising models on the cactus tree or on the usual lattice in the “cactus approximation”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 105(3), pages 620-630.
  • Handle: RePEc:eee:phsmap:v:105:y:1981:i:3:p:620-630
    DOI: 10.1016/0378-4371(81)90115-1
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437181901151
    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(81)90115-1?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. Shimada Haruo & Nishikawa Shunsaku, 1980. "Eine Analyse des japanischen Beschäftigungssystems und des Arbeitsmarktes für Jugendliche," Zeitschrift für Wirtschaftspolitik, De Gruyter, vol. 29(1), pages 71-90, January.
    2. Katsura, Shigetoshi & Nagahara, Izuru, 1980. "Effect of the frustration to the ground state energy and entropy of the spin-glass in the random bond Ising model on the square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(3), pages 397-416.
    Full references (including those not matched with items on IDEAS)

    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. Katsura, Shigetoshi & Matsuno, Akira, 1983. "The transition from the spin-glass to the ferromagnetic state in the bond-random Ising model in the face-centred cubic lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 483-488.
    2. Sannemo, U. & Chao, K.A., 1984. "Frustation in local environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(2), pages 605-608.
    3. Katsura, Shigetoshi & Kikuchi, Ryoichi, 1984. "The cluster variation method and the method of the reducibility of density matrices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(2), pages 595-604.
    4. Miyamoto, Nahomi & Katsura, Shigetoshi, 1982. "Entropy and free energy of the spin glass in the random-bond ising model on the square lattice at finite temperatures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 111(1), pages 1-16.

    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:105:y:1981:i:3:p:620-630. 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.