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Explicit thermostatics of Stanley's n-vector model on the harmonic chain by Fourier analysis

Author

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  • Junker, Georg
  • Leschke, Hajo
  • Zan, Ingbert

Abstract

Thermostatic properties of Stanley's classical n-vector model on the harmonic chain are studied. It is shown that this model belongs to a rather general class of classical spin models in one dimension. The members of this class are characterized by spins which are elements of a homogenous space with transformation group G and a G-invariant and exchange-invariant spin-pair interaction. For the derivation of basic thermostatic quantities and correlation functions we use the method of abstract Fourier analysis. This allows to derive rather explicit results for any member of the aforementioned class of spin models. We present an exact closed-form expression as well as a high- and a low-temperature expansion for the free energy of Stanley's n-vector model on the harmonic chain. From this basic thermostatic quantities like internal energy, entropy and heat capacity are obtained. Furthermore, we present results for expectation values of one-spin and two-spin functions. From the latter it is possible to derive the zero-field susceptibility and it also allows for a discussion of magnetostrictive effects.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:237:y:1997:i:1:p:257-284
    DOI: 10.1016/S0378-4371(96)00413-X
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    References listed on IDEAS

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    1. Claire K. Schultz, 1963. "A generalized computer method for information retrieval," American Documentation, Wiley Blackwell, vol. 14(1), pages 39-48, January.
    2. 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.
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