Group structure for classical lattice systems of arbitrary spin

  • A. Hintermann
  • C. Gruber
Classical Mechanics, Quantum Mechanics, Field Theory, Statistical Mechanics
Part of the Lecture Notes in Physics book series (LNP, volume 50)


We equip lattice systems of arbitrary spin with group structures. Harmonic analysis is used to derive low and high temperature expansions of the partition function as well as duality relations among different models.

The Asano contraction is formulated without using the Griffiths transformation into an equivalent spin 1/2 system. A necessary and sufficient condition is given to obtain the partition function as the Asano contraction of smaller systems. For a given system with spin p > 1/2, the group structure is not unique. The consequences of this fact are discussed in the case of spin 1 models for which we give analyticity domains.


Partition Function Group Structure Fourier Coefficient Duality Relation Arbitrary Spin 
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  1. [1]
    D. Merlini, C. Gruber, J.M.P. 13, (1972), 1814.CrossRefGoogle Scholar
  2. [2]
    W. Greenberg, Com. Math. Phys. 29, (1973), 163.CrossRefGoogle Scholar
  3. [3]
    C. Gruber, A. Hintermann, H.P.A. 47, (1974), 67Google Scholar
  4. [4]
    A. Hintermann, C. Gruber, in preparation.Google Scholar
  5. [5]
    D. Ruelle, Phys. Rev. Lett., 26, (1971), 303.CrossRefGoogle Scholar
  6. [6]
    J. Slawny, Com. Math. Phys., 34, (1973), 271.CrossRefGoogle Scholar
  7. [7]
    C. Gruber, A. Hintermann and D. Merlini, Com. Math. Phys. 40, (1975), 83.CrossRefGoogle Scholar
  8. [8]
    K.Y. Millard, K.S. Viswanathan, Phys. Rev. B, 9, (1974), 2030.CrossRefGoogle Scholar
  9. [9]
    K.Y. Millard, K.S. Viswanathan, J.M.P. 15, (1974), 1821.Google Scholar
  10. [10]
    J. Slawny, Ferromagnetic Spin Systems at Low Temperature,preprint.Google Scholar
  11. [11]
    D. Ruelle, Com. Math. Phys. 31, (1973), 265.Google Scholar
  12. [12]
    J.L. Lebowitz, G. Gallavotti, J.M.P. 12, (1971), 1129.Google Scholar
  13. [13]
    S. Sarbach, F. Rys, Phys. Rev. B, 7, (1973), 3141.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • A. Hintermann
    • 1
  • C. Gruber
    • 1
  1. 1.Laboratoire de Physique ThéoriqueEcole Polytechnique FédéraleLausanneSwitzerland

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