Journal of Statistical Physics

, Volume 20, Issue 3, pp 317–330 | Cite as

On a class of exactly soluble statistical mechanical models with nonpolynomial interactions

  • J. G. Brankov
  • N. S. Tonchev
  • V. A. Zagrebnov


The approximating Hamiltonian method of N. N. Bogolubov, Jr. is generalized to models with nonpolynomial intensive-observable interactions. The original Hamiltonian is proved to be thermodynamically equivalent to one linear in the intensive-observable trial Hamiltonian. We show that the exact expression for the free energy density in the thermodynamic limit can be obtained from a min-max principle for the system with trial Hamiltonian.

Key words

Approximating Hamiltonian method nonpolynomial interactions intensive observables thermodynamic equivalence 


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Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • J. G. Brankov
    • 1
  • N. S. Tonchev
    • 1
  • V. A. Zagrebnov
    • 1
  1. 1.Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaUSSR

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