Dominicis, C. de.
CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique1980
CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique1980
AbstractAbstract
[en] After a sketchy derivation of TAP equations, we show first how one can recover two known results (Sherrington Kirkpatrick, and Sommers) by direct perturbation resommation a la Martin Siggia Rose. Going beyond perturbation, it is recalled that TAP equations can be reduced to a one site self consistent problem involving several order parameters. The existence of a large number of solutions to TAP equations at low T forces us to choose a weight to be attributed to each solution. Also we are forced to reintroduce replicas to compute averages over the ensemble of solutions. In contradistinction to what usually occurs it is argued that here replicas are rather innocent. The uniform (white) average and the microcanonical average are briefly discussed
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Feb 1980; 13 p; Common trends in particle and condensed matter physics; Les Houches, France; 18 - 29 Feb 1980
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Dominicis, C. de
CEA Saclay, 91 - Gif-sur-Yvette (France)1961
CEA Saclay, 91 - Gif-sur-Yvette (France)1961
AbstractAbstract
[en] The grand partition function Z (α,β) of a quantum system is studied, using diagrammatic representations of the perturbation expansion. For a fermions system, it is possible to show, by proper resummation, without approximations but under some 'regularity hypothesis', that Log Z (α,β) takes a form where, besides trivial dependences, α and β only appear through a statistical factor Fk- = [1 + e-α+βεk0-βWk]-1. Wk is a (real) self-consistent potential, generalized to all orders and can be defined by a stationary condition on Log Z (α,β) under variations of Fk-. The thermodynamical quantities take a form analogous to the expressions Landau introduced for the Fermi liquids. The zero temperature limit (for isotropic systems) gives back Goldstone expressions for the ground state of a system. (author)
[fr]
La grande fonction de partition Z (α,β) d'un systeme quantique est etudiee en utilisant des representations diagrammatiques du developpement en serie des perturbations. Pour un systeme de fermions on peut, par des resommations adequates, sans approximations mais sous reserve d'une 'hypothese de regularite', mettre Log Z (α,β) sous une forme ou, en dehors de dependances triviales, α et β n'interviennent que par l'intermediaire d'un facteur statistique Fk- = [1 + e-α+βεk0-βWk]-1. Wk est ici un potentiel self-consistant (reel) generalise a tous les ordres et peut etre defini par une condition de stationnarite de Log Z (α,β) pour des variations de Fk-. Les grandeurs thermodynamiques prennent une forme analogue aux expressions que LANDAU a introduites pour les liquides de FERMI. A la limite de la temperature nulle (et pour un systeme isotrope) on retrouve terme a terme les expressions de GOLDSTONE relatives a l'etat fondamental d'un systeme. (auteur)Original Title
La grande fonction de partition Z (α,β) d'un systeme quantique est etudies en utilisant des representations diagrammatiques du developpement en serie des perturbations
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1961; 282 p; 54 refs.
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ANNIHILATION OPERATORS, BLOCH THEORY, CREATION OPERATORS, DELTA FUNCTION, FERMI GAS, FERMIONS, FREE ENTHALPY, GOLDSTONE DIAGRAMS, GROUND STATES, HAMILTONIAN FUNCTION, LANDAU QUASI PARTICLES, MANY-BODY PROBLEM, PARTICLE INTERACTIONS, PARTITION FUNCTIONS, PAULI PRINCIPLE, PERTURBATION THEORY, QUANTUM MECHANICS, SECOND QUANTIZATION, SLATER METHOD, STATISTICAL MECHANICS, TEMPERATURE ZERO K, THERMODYNAMICS, WAVE FUNCTIONS, WICK THEOREM
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Bloch, C.; Dominicis, C. de
CEA Saclay, 91 - Gif-sur-Yvette (France)1959
CEA Saclay, 91 - Gif-sur-Yvette (France)1959
AbstractAbstract
[en] A short account is given of some recent work on the perturbation expansion of the Gibbs potential of quantum statistical mechanics. (author)
[fr]
Expose en resume de quelques travaux sur le developpement dans la theorie des perturbations du potentiel de Gibbs de la Mecanique Statistique. (auteur)Original Title
Sur le developpement du potentiel de gibbs
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1959; 4 p; 8 refs.
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AbstractAbstract
[en] The dynamics of critical phenomena as is described by stochastic equations of the Landau-Ginzburg type with or without conservation law, is studied by the technique of field renormalization. The case of mode coupling systems is briefly touched upon
[fr]
La dynamique des phenomenes critiques telle qu'elle est decrite par les equations stochastiques de type Ginzburg-Landau dependant du temps, avec ou sans loi de conservation, est etudiee par les techniques de renormalisation de la theorie des champs. Le cas des systemes comportant un couplage mode-mode est brievement abordeOriginal Title
Techniques de renormalisation de la theorie des champs et dynamique des phenomenes critiques
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Colloquium critical phenomena; Dijon, France; 30 Jun 1975
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J. Phys. (Paris), Colloq; (no.1); p. C1.247-C1.253
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Almeida, J.R.L.; Dominicis, C. de
International Union of Pure and Applied Physics1989
International Union of Pure and Applied Physics1989
AbstractAbstract
[en] Published in summary form only
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1989; 1 p; 17. IUPAP International Conference on Thermodynamics and Stastical Mechanics; Rio de Janeiro, RJ (Brazil); 31 Jul - 4 Aug 1989; Available from the Library of the Comissao Nacional de Energia Nuclear, RJ, Brazil
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[en] Strong infrared divergences prevent standard spin glass field theory to be meaningful, at least below d=6. A mechanism that softens infrared divergences is displayed, that, via the existence of a sea of zero or near zero modes, relates softening in infrared divergences and in the samll x behavior of Parisi order parameter q(x). This mechanism may, hopefully, allow the building of a meaningful spin glass field theory in the condensed phase. (orig.)
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17. IUPAP international conference on thermodynamics and statistical mechanics (STATPHYS-17); Rio de Janeiro, RJ (Brazil); 31 Jul - 4 Aug 1989
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Dominicis, C. de
CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique1989
CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique1989
AbstractAbstract
[en] In this work we show that a class of Ising spin glass models with finite connectivity exhibits instability when replica symmetry is not broken in the condensed phase at low temperatures. These models are relevant for complex optimization problems and may also give important insights about real spin-glasses
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1989; 10 p; Meeting on New Trends in Magnetism; Recife, PE (Brazil); 25-28 Jul 1989
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Pimentel, I R; Dominicis, C De, E-mail: irpimentel@fc.ul.pt, E-mail: cirano.de-dominicis@cea.fr2014
AbstractAbstract
[en] We develop a field theory for spin glasses using replica Fourier transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas n and the number of replica symmetry breaking steps R generic integers. We show how the RFT applied to the two-replica fields allows one to construct a new basis which block-diagonalizes the four-replica mass-matrix, into the replicon, anomalous and longitudinal modes. The eigenvalues are given in terms of the mass RFT and the propagators in the RFT space are obtained by inversion of the block-diagonal matrix. The formalism allows one to express any i-replica vertex in the new RFT basis and hence enables one to perform a standard perturbation expansion. We apply the formalism to calculate the contribution of the Gaussian fluctuations around the Parisi solution for the free-energy of an Ising spin glass. (paper)
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Available from http://dx.doi.org/10.1088/1751-8113/47/45/455001; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
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Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121;
; v. 47(45); [34 p.]

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