<i>The Quantum Mechanics of Many-Body Systems</i>

Thouless, D. J.; Massey, H. S. W.; Hellwarth, R. W.

doi:10.1063/1.3058273

Cited by 233 publications

(416 citation statements)

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“…In this section, we analyze the effect of the quartic terms in the action on the stability of the free fermion spectrum at zero mass, along the critical line g 0 = t 2 + 2t − 1, by considering the effect of the interaction part of the action onto the kinetic part within the HFB like approximating scheme [46,47,48]. The Ising part can be easily written in the momentum space representation, which we will also refer to as Fourier space, after having defined the ∆ 0…”

Section: Tricritical Point: Hartree-fock-bogoliubov Analysismentioning

confidence: 99%

“…The point is that in the BC case the effective stiffness coefficient vanishes at some position at the critical line, for a sufficiently strong dilution, which may eventually be identified as the tricritical point of the BC model. In what follows, we apply the Hartree-Fock-Bogoliubov (HFB) approximating scheme [46,47,48] in the momentum space in order to gain a modification of the above Ising like behaviour provided by the presence of the interaction in the BC case. In essence, the HFB decouples the four-fermion interaction into few Gaussian terms added to the basic action.…”

Section: Effective 2nd Order Fermionic Field Theorymentioning

confidence: 99%

“…At the tricritical point, we assume that the effective stiffness coefficient in factor Z k also vanishes. The Hartree-Fock-Bogoliubov (HFB) approximation scheme will be used to count properly the effects of the interaction [46,47,48].…”

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confidence: 99%

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Alternative description of the 2D Blume–Capel model using Grassmann algebra

Clusel¹,

Fortin²,

Plechko³

2008

J. Phys. A: Math. Theor.

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Abstract. We use Grassmann algebra to study the phase transition in the twodimensional ferromagnetic Blume-Capel model from a fermionic point of view. This model presents a phase diagram with a second order critical line which becomes first order through a tricritical point, and was used to model the phase transition in specific magnetic materials and liquid mixtures of He 3 -He 4 . In particular, we are able to map the spin-1 system of the BC model onto an effective fermionic action from which we obtain the exact mass of the theory, the condition of vanishing mass defines the critical line. This effective action is actually an extension of the free fermion Ising action with an additional quartic interaction term. The effect of this term is merely to render the excitation spectrum of the fermions unstable at the tricritical point. The results are compared with recent numerical Monte-Carlo simulations.

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Section: Tricritical Point: Hartree-fock-bogoliubov Analysismentioning

confidence: 99%

Section: Effective 2nd Order Fermionic Field Theorymentioning

confidence: 99%

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Alternative description of the 2D Blume–Capel model using Grassmann algebra

Clusel¹,

Fortin²,

Plechko³

2008

J. Phys. A: Math. Theor.

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“…When A h n d B" (x = s, t) are real, we can further factorize the Hessian [3] and instead consider the matrices (1,2) The relationship between the eigenvectors of [3] and [5] is easily found (1,2,28). Finally, designating the eigenvector of [3] as a function of the mixing parameter K .…”

Section: Singlet and Non-singlet Stability Conditionsmentioning

confidence: 99%

“…Finally, designating the eigenvector of [3] as a function of the mixing parameter K . In other words, the eigenvector components ~l,,~, = d,, give the ratios in which the virtual orbitals must be admixed to the occupied orbitals in order to obtain a trial function corresponding to the direction of the steepest descent (slowest ascent) at the studied point represented by Qo ( I , 2, 28).…”

Section: Singlet and Non-singlet Stability Conditionsmentioning

confidence: 99%

Hartree–Fock stability and symmetry breaking: oxygen doubly negative ion

Paldus¹,

Čı́žek²

1985

Can. J. Chem.

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The Hartree-Fock stability problem, its relationship to the broken symmetry solutions, and the implications for a molecular nuclear framework distortion are briefly reviewed. The case where no nuclear framework distortion is possible is studied for the oxygen doubly negative ion, using an ab itzitio Slater-type orbital analytical approach, in order to illustrate other possible implications of the symmetry breaking in the independent particle models. It is shown that the existing pure singlet broken symmetry solutions for this ten electron ion, which were obtained earlier by ad hoc procedures, follows systematically and straightforwardly from the HF stability problem for the corresponding symmetry adapted solution which shows a strong singlet instability. The chemical and physical implications of this type of symmetry breaking are briefly discussed.Can. J. Chem. 63, 1803 ((985). On passe brikvement en revue le problkme de la stabilitC des solutions des equations de Hartree-Fock. On a mis en evidence le rble des solutions de symktrie brisCe et les implications par rapport une distorsion du squelette nucliaire moleculaire. Dans le but d'illustrer d'autres implications possibles du bris de symktrie dans le modkle a particules independantes, on a utilisk une approche analytique ab irritio avec des orbitales du type de Slater pour Ctudier l'ion doublement nCgatif de I'oxygene, un cas ou il n'y a pas de possibilitC de distorsion du squelette nuclCaire. On dkmontre que, pour cet ion a dix Clectrons, les solutions de symCtrie brisCe correspondant ides singulets purs, qui ont Ctt obtenues antirieurement par des procCdures nrl hoc, dCcoulent systkmatiquement et d'une facon directe du problkme de la stabilitt HF. La solution correspondante adaptCe pour la symCtrie posskde une instabilitk forte du type singulet. On discute brievement des implications chimiques et physiques de ce type de bris de symCtrie.[Traduit par le journal]

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Valence States of BeO Feynman's Way

Sorensen¹,

England²

2000

Int. J. Quant. Chem.

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Energy curves are computed by adding a second‐order Feynman diagram to a zero of energy. Third order confirms the goodness of second order. The zero of energy includes charge transfer and polarization. It is an average of a limited configuration‐mixing model. Evaluation of diagrams requires one set of model orbitals for all valence states, one set of probability amplitudes for all valence states, and two parameters for each valence state. Parameters are evaluated with the zero of energy. Spectroscopic constants and excitation and dissociation energies approach limits of the chosen basis set. Average (maximum) errors between second order and experiment for X, a, A, and B are 0.9 (2.1) pm for Re; 17 (31) kJ/mol for De; 2 (6) kJ/mol for Te; 35 (45) cm−1 for ωe; and 9 (21) kJ/mol for T∞. Frequencies and bond distances for C do not match any calculated for a single state. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 259–279, 2000

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The Quantum Mechanics of Many-Body Systems

Cited by 233 publications

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Alternative description of the 2D Blume–Capel model using Grassmann algebra

Alternative description of the 2D Blume–Capel model using Grassmann algebra

Hartree–Fock stability and symmetry breaking: oxygen doubly negative ion

Valence States of BeO Feynman's Way

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