IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v84y1976i2p336-349.html
   My bibliography  Save this article

The classical one-dimensional Heisenberg magnet in an external magnetic field. Transfer matrix formalism as an application of renormalization group theory “avant la lettre”

Author

Listed:
  • Ruijgrok, Th.W.
  • Niemeijer, Th.

Abstract

The classical one-dimensional Heisenberg magnet is treated in the context of renormalization theory. This treatment is shown to be equivalent to the usual transfer matrix approach. If the chain consists of N spins, the original hamiltonian will, upon repeated application of the renormalization transformation, be transformed into N uncoupled spins described by N identical one-particle hamiltonians, Heff, which depends upon the original interaction and field.

Suggested Citation

  • Ruijgrok, Th.W. & Niemeijer, Th., 1976. "The classical one-dimensional Heisenberg magnet in an external magnetic field. Transfer matrix formalism as an application of renormalization group theory “avant la lettre”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(2), pages 336-349.
    • Handle: RePEc:eee:phsmap:v:84:y:1976:i:2:p:336-349
    DOI: 10.1016/0378-4371(76)90005-4
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437176900054
    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(76)90005-4?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. Rao, C. H. Hanurmantha & Subbarao, K., 1976. "Marketing of Rice in India: An Analysis of the Impact of Producers' Prices on Small Farmers," Indian Journal of Agricultural Economics, Indian Society of Agricultural Economics, vol. 31(2), April.
    2. Niemeijer, Th. & Ruijgrok, Th.W., 1975. "Renormalization group solution of the one-dimensional classical Heisenberg model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 81(3), pages 427-440.
    3. Irene Lurie, 1975. "Work or Welfare? Factors in the Choice for AFDC Mothers by Mildred Rein," Journal of Human Resources, University of Wisconsin Press, vol. 10(3), pages 407-409.
    4. Vincent P. Houghton & Tony E. Gear, 1975. "Towards a Management Science Perspective for Recurrent Education," Interfaces, INFORMS, vol. 5(2), pages 1-10, February.
    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. Junker, Georg & Leschke, Hajo & Zan, Ingbert, 1997. "Explicit thermostatics of Stanley's n-vector model on the harmonic chain by Fourier analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(1), pages 257-284.
    2. Hu, Bambi, 1979. "Renormalization group study of the one dimensional quantum mechanical XY model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(1), pages 330-336.
    3. Rogiers, J., 1982. "Direct estimates for η from series analysis for several lattice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(1), pages 303-314.
    4. Niemeijer, Th. & Ruijgrok, Th.W., 1977. "Phase transition in a linear chain of classical spins with a logarithmic nearest neighbour pair potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 86(1), pages 200-204.
    5. Antle, John M., 1982. "Infrastructure and Agricultural Productivity: Theory, Evidence and Implication for Growth and Equity in Agricultural Development," 1982 Conference, August 24-September 2, 1982, Jakarta, Indonesia 182447, International Association of Agricultural Economists.
    6. 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.
    7. Nightingale, M.P, 1975. "Scaling theory and finite systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 83(3), pages 561-572.
    8. Van Dieren, F. & Van Leeuwen, J.M.J., 1986. "Renormalization of the gas-liquid transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 136(1), pages 21-46.

    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:84:y:1976:i:2:p:336-349. 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.