IDEAS home Printed from https://ideas.repec.org/a/hin/jijmms/371643.html
   My bibliography  Save this article

Two dimentional lattice vibrations from direct product representations of symmetry groups

Author

Listed:
  • J. N. Boyd
  • P. N. Raychowdhury

Abstract

Arrangements of point masses and ideal harmonic springs are used to model two dimensional crystals. First, the Born cyclic condition is applied to a double chain composed of coupled linear lattices to obtain a cylindrical arrangement. Then the quadratic Lagrangian function for the system is written in matrix notation. The Lagrangian is diagonalized to yield the natural frequencies of the system. The transformation to achieve the diagonalization was obtained from group theorectic considerations. Next, the techniques developed for the double chain are applied to a square lattice. The square lattice is transformed into the toroidal Ising model. The direct product nature of the symmetry group of the torus reveals the transformation to diagonalize the Lagrangian for the Ising model, and the natural frequencies for the principal directions in the model are obtained in closed form.

Suggested Citation

  • J. N. Boyd & P. N. Raychowdhury, 1983. "Two dimentional lattice vibrations from direct product representations of symmetry groups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:371643
    DOI: 10.1155/S0161171283000666
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJMMS/6/371643.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJMMS/6/371643.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/S0161171283000666?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
    ---><---

    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:hin:jijmms:371643. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.