Heisenberg model with long range interaction☆

https://doi.org/10.1016/0022-3697(65)90233-7Get rights and content

Abstract

The functional Integral method as used by Siegert in his study of the Ising Model with long range interaction, is generalized and applied to the Heisenberg model. Above the Bragg-Williams Curie point, the functional integral expression for the partition function is evaluated by a saddle point approximation. This gives us an expansion in powers of the reciprocal range of the interaction which is essentially identical with the Ising Model result, in agreement with Brout who used a ring summation approximation. The expansion is not valid through the Curie point, and in its present form, our method seems to be incapable of giving spin waves.

References (13)

  • M. Kac

    Phys. Fluids

    (1959)
    M. Kac

    Studies in Mathematical Analysis and Related Topics: Essays in Honor of George Polya

    (1962)
    G.A. Baker

    Phys. Rev.

    (1961)
  • M. Kac et al.

    J. Math. Phys.

    (1963)
  • M. Kac et al.

    J. Math. Phys.

    (1963)
    M. Kac et al.

    J. Math. Phys.

    (1963)
    M. Kac et al.

    J. Math. Phys.

    (1964)
    G.E. Uhlenbeck
  • R. Brout

    Phys. Rev.

    (1960)
  • R. Brout

    Phys. Rev.

    (1959)
    R. Brout

    Phys. Rev.

    (1961)
    G. Horwitz et al.

    Phys. Rev.

    (1961)
    F. Englert

    Phys. Rev.

    (1963)
  • A.J.F. Siegert
There are more references available in the full text version of this article.

Cited by (0)

☆

Supported by U.S. Air Force Office of Scientific Research, under AF Grant No. AF-AFOSR-610-64, Theory of Solids.

†

Address from September: The Rockefeller Institute, New York, New York 10021.

View full text
Copyright © 1965 Published by Elsevier Ltd.