Advertisement

Pseudo equilibrium description of disordered systems

  • G. Sobotta
III. Random Systems
Part of the Lecture Notes in Physics book series (LNP, volume 206)

Abstract

We discussed the pseudo equilibrium description of quenched random systems. By generalizing the grand canonical ensemble it was possible to take into account frozen in spatial distributions of atoms on a lattice. The difference to the grand canonical ensemble for annealed systems is given by additional chemical potentials or forces of constraints, which are conjugated to the momenta of the occupation numbers. The obtained description is completely equivalent to the conventional description, based on the configurational average of the free energy. However, the construction of a partition function or generating functional allows to apply successful methods, which have been developed for equilibrium systems, to treat quenched disordered systems. The experience from field theoretical investigations of random ferromagnets13, which are briefly discussed in a second article in this volume14, seems to indicate that the pseudo equilibrium description of disordered systems may be applied also for further problems as for instance the localization phenomena.

Although this method has been discovered3 and rediscovered15 to perform concrete calculations, it has been considered also for more general investigations to understand the difference between annealed and quenched systems 5. Because the forces of constraints delivers a quantitative information upon the interaction of the spins with the occupation numbers, it was possible to check to validity of an ideal quenched model. Obviously, diverging spin energy fluctuations show that the assumption of ideal quenching may be rather unphysical.

Keywords

Partition Function Occupation Number Thermodynamical Potential Grand Canonical Ensemble Random System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Brout, Phys. Rev. 115 (1959) 824MATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    G. Grinstein and A. Luther, Phys. Rev. B13 (1975) 1329; V.J.Emery, Phys. Rev. B11 (1975) 239; A. Aharony, Phys. Rev. B12 (1975) 1038ADSGoogle Scholar
  3. 3.
    T. Morita, J. Math. Phys. 5 (1964) 1401CrossRefADSGoogle Scholar
  4. 4.
    G. Sobotta and D. Wagner, Z.Phys. B33 (1979) 271ADSGoogle Scholar
  5. 5.
    J.C. Wheeler and R.B. Griffiths, Phys. Rev. 170 (1968) 249CrossRefADSGoogle Scholar
  6. 6.
    S.F. Edwards and P.W. Anderson, J. Phys. F5 (1975) 965CrossRefADSGoogle Scholar
  7. 7.
    M.F. Thorpe and D. Beeman, Phys. Rev. B14 (1976) 188; see also M.F. Thorpe, J.Phys. C11 (1978) 2986; H. Falk, J. Phys. C9 (1976) L 213ADSGoogle Scholar
  8. 8.
    A. Huber and R. Kühn, DPG-Frühjahrstagung, Freudenstadt 1983Google Scholar
  9. 9.
    G. Sobotta, DPG-Frühjahrstagung, Freudenstadt 1983Google Scholar
  10. 10.
    G. Sobotta, J. Magn. Magn. Mat. 28 (1982) 1CrossRefADSGoogle Scholar
  11. 11.
    B. Griffiths, Phys. Rev. Lett. 23 (1969) 17CrossRefADSGoogle Scholar
  12. 12.
    M. Wortis, Phys. Rev. B10 (1974) 4665; Y. Imry, Phys.Rev. B15 (1977) 4448ADSGoogle Scholar
  13. 13.
    G. Sobotta and D. Wagner, J. Phys. C11 (1978) 1467; see also ref. 4; for a review see G. Sobotta and D. Wagner, DPG-Frühjahrstagung, Münster 1984, to be published in J. Magn. Magn. Mat.ADSGoogle Scholar
  14. 14.
    K. Westerholt and G. Sobotta, this volumeGoogle Scholar
  15. 15.
    G. Sobotta and D. Wagner, J.Magn. Magn. Mat. 6 (1977) 92; see alsoCrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • G. Sobotta
    • 1
  1. 1.Institut für Theoretische Physik IIIRuhr-Universität BochumBochumGermany

Personalised recommendations