Generalized Molecular Fields

Marsh, James S.

doi:10.1103/physrev.178.403

Cited by 2 publications

(3 citation statements)

References 9 publications

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“…These depend on the alloy component and total densities of states, the phonon Green function, and the parameters of the model. To summarize, various schemes of "effective mean-field theory" taking into account correlations were proposed [35,36,37,96,97,98,99,100,101,102,103,104,105,106]. The main efforts were directed to the aim to describe suitably the collective behavior of particles in terms of effectivefield distribution which satisfies a self-consistent condition.…”

Section: The Mean Field Conceptmentioning

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: The Mean Field Conceptmentioning

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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“…One can use this solution to get a better approximation than the mean field theory. There are some other methods of improvement of the molecular field theory [72], [73]. Unfortunately, these approaches are nonsystematic.…”

Section: Generalized Mean Fieldsmentioning

confidence: 99%

“…Moreover, the superconductor is a system in which the interaction between electrons qualitatively changes the spectrum of excitations. However, quasiparticles are still of use even in this case, due to the correct redefinition of the relevant generalized mean field which includes the anomalous averages (see (72)). In a strongly interacted system on a lattice with complex spectra, the concept of a quasi-particle needs a suitable adaptation and a careful examination.…”

Section: Green Function Picture Of Quasi-particlesmentioning

confidence: 99%

Irreducible Green functions method and many-particle interacting systems on a lattice

Kuzemsky

2002

Riv. Nuovo Cim.

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The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions (GFs) is presented. This method was developed to overcome some ambiguities in terminating the hierarchy of the equations of motion of double-time Green functions and to give a workable technique to systematic way of decoupling. The approach provides a practical method for description of the many-body quasi-particle dynamics of correlated systems on a lattice with complex spectra. Moreover, it provides a very compact and self-consistent way of taking into account the damping effects and finite lifetimes of quasi-particles due to inelastic collisions. In addition, it correctly defines the Generalized Mean Fields (GMF), that determine elastic scattering renormalizations and , in general, are not functionals of the mean particle densities only. The purpose of this article is to present the foundations of the IGF method. The technical details and examples are given as well. Although some space is devoted to the formal structure of the method, the emphasis is on its utility. Applications to the lattice fermion models such as Hubbard/Anderson models and to the Heisenberg ferro-and antiferromagnet, which manifest the operational ability of the method are given. It is shown that the IGF method provides a powerful tool for the construction of essentially new dynamical solutions for strongly interacting many-particle systems with complex spectra.

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Generalized Molecular Fields

Cited by 2 publications

References 9 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

Irreducible Green functions method and many-particle interacting systems on a lattice

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