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Systems with separable many-particle interactions. I

Author

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  • den Ouden, L.W.J.
  • Capel, H.W.
  • Perk, J.H.H.
  • Tindemans, P.A.J.

Abstract

In this paper we give an exact evaluation of the free energy per particle for systems with separable many-particle interactions described by a hamiltonian of the type H = ∑kT(k) + NP (N-1 ∑k V(k)), where P is an arbitrary polynomial. In the proof use is made of a fundamental theorem due to Bogoliubov Jr. for ferromagnetic quadratic operators. The free energy can be obtained from a trial hamiltonian, which is linear in the operators T and V.

Suggested Citation

  • den Ouden, L.W.J. & Capel, H.W. & Perk, J.H.H. & Tindemans, P.A.J., 1976. "Systems with separable many-particle interactions. I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(1), pages 51-70.
    • Handle: RePEc:eee:phsmap:v:85:y:1976:i:1:p:51-70
    DOI: 10.1016/0378-4371(76)90118-7
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    References listed on IDEAS

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    1. Barend A. De Vries, 1972. "International Price Comparisons of Selected Capital Goods Industries," NBER Chapters, in: International Comparisons of Prices and Output, pages 335-367, National Bureau of Economic Research, Inc.
    2. Brankov, J.G. & Tonchev, N.S. & Zagrebnov, V.A., 1975. "An exactly solvable model for metal-insulator phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 79(1), pages 125-127.
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    Cited by:

    1. Nijhoff, F.W. & Capel, H.W., 1981. "Separable interactions and liquid 3He," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 106(3), pages 369-397.
    2. Nijhoff, F.W. & Capel, H.W. & Den Breems, A., 1986. "Separable interactions and liquid 3He," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(2), pages 295-327.
    3. Capel, H.W. & Schakel, Adriaan M.J., 1989. "Symmetry breaking patterns in superfluid 3He," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(3), pages 409-441.
    4. Capel, H.W. & Nijhoff, F.W. & Den Breems, A., 1986. "Separable interactions and liquid 3He," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 139(2), pages 256-305.
    5. Falk, H. & Falk, C.T., 1978. "Data cluster analysis: Abrupt transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 90(2), pages 325-332.
    6. Capel, H.W. & Den Ouden, L.W.J. & Perk, J.H.H., 1979. "Stability of critical behaviour, critical-exponent renormalization and first-order transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 95(3), pages 371-416.
    7. Shumovsky, A.S. & Yukalov, V.I., 1982. "Exact solutions for heterophase ferromagnets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 110(3), pages 518-534.
    8. Perk, J.H.H. & Capel, H.W. & den Ouden, L.W.J., 1977. "Convex-envelope formulation for separable many-particle interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 89(3), pages 555-568.
    9. Maćkowiak, J., 1983. "On the exact mean-field description of continuous quantum systems in equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(1), pages 47-75.
    10. Maćkowiak, J., 1983. "On the exact mean-field description of continuous quantum systems in equilibrium II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(1), pages 59-84.
    11. Nijhoff, F.W. & Capel, H.W. & Den Breems, A., 1985. "Separable interactions and liquid 3He," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(3), pages 375-411.
    12. Maćkowiak, J., 1985. "A solvable model of an anisotropic superconductor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 133(3), pages 509-530.
    13. Maćkowiak, J., 1982. "On the mean field description of systems of point particles in equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 110(1), pages 302-320.
    14. Brussaard, P. & van Weert, Ch.G., 1996. "Effective action for the superfluid Fermi gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 228(1), pages 102-114.
    15. Bakulev, A.P. & Bogoljubov, N.N. & Kurbatov, A.M., 1986. "Rigorous results in the theory of superconductivity with Coulomb-like repulsion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 134(2), pages 359-376.

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