IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v99y1979i1p193-216.html
   My bibliography  Save this article

Spin glasses for the infinitely long ranged bond Ising model and for the short ranged binary bond Ising model without use of the replica method

Author

Listed:
  • Katsura, Shigetoshi
  • Inawashiro, Sakari
  • Fujiki, Sumiyoshi

Abstract

The long ranged Gaussian random Ising bond model and short ranged binary random Ising bond model are discussed by the method of the pair approximation of the cluster variation and by the method of the integral equation for the distribution function of the effective fields. For the long ranged model, Sherrington and Kirkpatrick's result is generalized and rederived without use of the replica method. For the short ranged model, i.e. a binary mixture of JA = -JB, the integral equation is solved exactly and the energy of the spin glass state is obtained at T = 0.

Suggested Citation

  • Katsura, Shigetoshi & Inawashiro, Sakari & Fujiki, Sumiyoshi, 1979. "Spin glasses for the infinitely long ranged bond Ising model and for the short ranged binary bond Ising model without use of the replica method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(1), pages 193-216.
    • Handle: RePEc:eee:phsmap:v:99:y:1979:i:1:p:193-216
    DOI: 10.1016/0378-4371(79)90130-4
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437179901304
    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(79)90130-4?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. Storing, Herbert J. & Strauss, Leo & Berns, Walter & Storing, Herbert J. & Weinstein, Leo & Horwitz, Robert, 1963. "Replies to Schaar and Wolin: I," American Political Science Review, Cambridge University Press, vol. 57(1), pages 151-160, March.
    2. Kirkpatrick, Jeane, 1975. "Representation in the American National Conventions: the Case of 1972," British Journal of Political Science, Cambridge University Press, vol. 5(3), pages 265-322, July.
    3. Morita, T. & Horiguchi, T., 1975. "Classical one-dimensional Heisenberg model with an interaction of finite range," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 83(3), pages 519-532.
    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. 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.
    2. Morita, T., 1984. "Spin-glass and ferromagnetic phases of the random-bond Ising model on the Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 321-343.
    3. Katsura, Shigetoshi & Miyamoto, Nahomi, 1982. "Random Ising model in the magnetic field at T = 0," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 393-404.
    4. Morita, T., 1983. "Free energy of the random Ising model in terms of the magnetizations of sites," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 143-152.
    5. Horiguchi, Tsuyoshi, 1981. "On the bethe approximation for the random bond Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 107(2), pages 360-370.
    6. Shirakura, Takayuki & Katsura, Shigetoski, 1983. "Spin glass in the infinitely long-ranged bond-random anisotropic classical planar model-longitudinal and transverse spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(2), pages 281-299.
    7. 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.
    8. Sasaki, Mitsuhiro & Katsura, Shigetoshi, 1989. "The asymmetric continuous distribution function of the effective field of the Ising model in the spin glass and the ferromagnetic states on the Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(3), pages 1195-1202.
    9. Akagi, Eiichi & Seino, Mitsuhiro & Katsura, Shigetoshi, 1991. "The free energy at T = 0 of the spin glass in the case of the continuous distribution of the effective field on the Bethe lattice for Z = 4, 5, 6," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(3), pages 406-414.
    10. de Oliveira, Mário J., 1988. "Ising spin glass in a field zero temperature in the Bethe approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 150(3), pages 614-626.
    11. Katsura, Shigetoshi & Suenaga, Toshiyuki & Imaizumi, Takahiro, 1982. "The boundary between the spin-glass and ferromagnetic states of the bond-random Ising model in the square lattice at T = 0," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(3), pages 368-379.
    12. Katsura, Shigetoshi, 1980. "Entropy of the spin-glass state in the binary mixture of the ferro- and antiferromagnetic random Ising model at T = 0," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(1), pages 333-338.
    13. de Oliveira, M.J., 1988. "Ising spin glass in the Bethe approximation at zero temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 148(3), pages 567-574.

    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 & 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.
    2. Akagi, Eiichi & Seino, Mitsuhiro & Katsura, Shigetoshi, 1991. "The free energy at T = 0 of the spin glass in the case of the continuous distribution of the effective field on the Bethe lattice for Z = 4, 5, 6," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(3), pages 406-414.
    3. Sibani, Paolo & Andersson, Jan-Olov, 1994. "Excitation morphology of short range Ising spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(1), pages 1-12.
    4. Ilkovič, V., 1996. "Cluster expansion for the spin-32 Blume-Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 234(1), pages 545-553.
    5. Tanaka, Yoshiaki & Uryŭ, Norikiyo, 1981. "A new method for calculation of the magnetic properties in one- and two-dimensional spin systems with anisotropic Heisenberg exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 105(3), pages 493-516.
    6. Kanter, I. & Shvartser, M., 1993. "The binary perceptron and general aspects of non-self-averaged quantities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 670-678.
    7. Katsura, Shigetoshi, 1980. "Entropy of the spin-glass state in the binary mixture of the ferro- and antiferromagnetic random Ising model at T = 0," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(1), pages 333-338.
    8. Chakraborty, K.G. & Morita, T., 1985. "A spin-one Ising model on the Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(2), pages 415-422.
    9. Shirakura, Takayuki & Katsura, Shigetoski, 1983. "Spin glass in the infinitely long-ranged bond-random anisotropic classical planar model-longitudinal and transverse spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(2), pages 281-299.
    10. Anglès d'Auriac, J.C. & Maillard, J.M. & Wu, F.Y., 1991. "Three-state chiral Potts models on the triangular lattice: a Monte Carlo study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 179(3), pages 496-506.
    11. Hassan, R.A. & Cieplak, Marek & Suan Li, Mai, 1993. "Quadrupolar and S = 1 Ising spin glasses in local mean field approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 192(1), pages 1-13.
    12. 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.
    13. Chen, Shyh-Tzer, 1996. "Mean-field renormalization group for the q-state clock spin-glass model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 229(2), pages 181-187.
    14. Morita, T., 1983. "Free energy of the random Ising model in terms of the magnetizations of sites," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 143-152.
    15. Dotsenko, V.S. & Tirozzi, B., 1992. "Replica-symmetry breaking in neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 385-394.
    16. Nusser, H. & Wagner, M., 1979. "Cluster expansions in cooperative Jahn-Teller T-systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 118-138.
    17. Canning, Andrew, 1992. "A class of long range Ising spin models described by Curie-Weiss mean field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 254-260.
    18. Pirc, R. & Tadić, B. & Blinc, R., 1992. "Proton and deutron glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 322-330.
    19. Morita, T., 1984. "Spin-glass and ferromagnetic phases of the random-bond Ising model on the Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 321-343.
    20. Yokota, Terufumi, 1992. "Numerical study of the TAP equations for infinite-range spin glass models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 336-339.

    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:99:y:1979:i:1:p:193-216. 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.