An Approximate Method for the Free Energy

Ferreira, J. R. Faleiro; Silva, N. P.

doi:10.1002/pssb.2221180240

Cited by 5 publications

(2 citation statements)

References 6 publications

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“…Prato and Barraco [148] presented a proof of the Bogoliubov inequality that does not require of the Baker-Campbell-Hausdorff expansion. Several variational approaches for the free energy have been proposed [152,153] as attempts to improve results obtained through the well established Bogoliubov principle. This principle requires the use of a trial Hamiltonian depending on one or more variational parameters.…”

Section: Variational Principle Of Bogoliubovmentioning

confidence: 99%

Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems

Kuzemsky

2015

Int. J. Mod. Phys. B

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The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising, Heisenberg and Hubbard models, superconducting (SC) and superfluid systems, etc. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects and for those who are interested in concrete applications. particle interacting systems; the variational principle of Bogoliubov; Bogoliubov inequality; generalized mean fields; model Hamiltonians of many-particle interacting systems. PACS numbers: 05.30-d, 05.30.Fk, 05.30.Jp, 05.70.-a, 05.70.Fh, 02.90.+p 1530010-1 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only. 1530010-2 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only. 1530010-5 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only. 1530010-8 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only. 1530010-9 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only.

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Section: Variational Principle Of Bogoliubovmentioning

confidence: 99%

Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems

Kuzemsky

2015

Int. J. Mod. Phys. B

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“…V as a sum of M divisions each one containing n sites, the arbitrary operator D is chosen as 1Tf D = D,, , with D , = eup (-pV,)/(exp (--BV,)), (8) m and is a n approximation assumed in order to (D), = 1.…”

Section: One Of the Approximations Suggested By Faleiro Ferreira And mentioning

confidence: 99%

An Improved Linear Chain Approximation for the Free Energy

Ferreira¹

1989

Physica Status Solidi (b)

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Some previous results obtained through a new variational approach recently proposed can be improved by using a sum of linear chains ss the trial Hsmiltonian. That approximation preserves short-range order effects above the approximate critical temperature.Einige vorlllufige Ergebnisse, die mit einem neuen kurzlich vorgeschlagenen Variationsverfahren erhalten werden, lassen sich durch Benutzung einer Summe linearer Ketten als Versuchs-Hamiltonoperator verbessern. Diese Naherung bewahrt Nahordnungseffekte oberhalb der kritischen Niiherungstemperatur.') Caixa Postal 702, 30161 Belo Horizonte-MG, Brazil. 2, Work partly supported by CNPq (Brazilian Agency).

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Critical Temperature of a Quasi‐One‐Dimensional Ising Model. The Bethe‐Peierls Approximation

Yurishchev

1985

Physica Status Solidi (b)

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An Approximate Method for the Free Energy

Cited by 5 publications

References 6 publications

Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems

Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems

An Improved Linear Chain Approximation for the Free Energy

Critical Temperature of a Quasi‐One‐Dimensional Ising Model. The Bethe‐Peierls Approximation

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