Interpolation method for the many-body problem

L. Kijewski, J. K. Percus

Research output: Contribution to journalArticlepeer-review


Variational principles for lower bounds to the energy, or free energy for T > 0°, of many-body systems are obtained in a form requiring density matrix minimization subject to certain model restrictions. The latter restrict the domain in which the density matrices can vary, and only utilize the energy - or free energy - for the model Hamiltonian HM. Increasingly accurate bounds are obtained as the model system begins to resemble the system of interest, and the behavior of the error as H - HM approaches zero is shown by two examples based upon the Ising model. Coupling the lower bound principle for the free energy with the standard Gibbs-Bogoliubov upper bound principle results in bounds on generalized susceptibility as well.

Original languageEnglish (US)
Pages (from-to)2184-2193
Number of pages10
JournalJournal of Mathematical Physics
Issue number11
StatePublished - 1967

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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