### Abstract

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 H_{M}. Increasingly accurate bounds are obtained as the model system begins to resemble the system of interest, and the behavior of the error as H - H_{M} 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 language | English (US) |
---|---|

Pages (from-to) | 2184-2193 |

Number of pages | 10 |

Journal | Journal of Mathematical Physics |

Volume | 8 |

Issue number | 11 |

State | Published - 1967 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*8*(11), 2184-2193.

**Interpolation method for the many-body problem.** / Kijewski, L.; Percus, Jerome.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 8, no. 11, pp. 2184-2193.

}

TY - JOUR

T1 - Interpolation method for the many-body problem

AU - Kijewski, L.

AU - Percus, Jerome

PY - 1967

Y1 - 1967

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36849100771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849100771&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36849100771

VL - 8

SP - 2184

EP - 2193

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 11

ER -