Erratum: “Two-Time Green's Functions and the Spectral Density Method in Nonextensive Classical Statistical Mechanics”[Phys. Rev. Lett. 87, 240602 (2001)]

Cavallo, A.; Cosenza, F.; Cesare, L. De

doi:10.1103/physrevlett.88.099901

Cited by 6 publications

(20 citation statements)

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“…(27) and the sum rule (25), one can get another general result which, as in the extensive case, may play a relevant role in practical calculations involving the q GFs.…”

Section: Mechanicsmentioning

confidence: 88%

“…In classical nonextensive thermostatistics, the two-time q GFs involving two classical observables are defined by [27] …”

Section: Appendix A: Two-time Green's Functions and Spectral Den-sitymentioning

confidence: 99%

“…Actually, starting from the definitions of Poisson's brackets and q mean value, it can be shown that [27] …”

Section: Appendix A: Two-time Green's Functions and Spectral Den-sitymentioning

confidence: 99%

“…Thus, many-body methods which allow one to perform direct calculations of the qproperties, overcoming the a priori knowledge of the related extensive ones, are desirable. Motivated by the conviction that a direct q GF method may provide new and effective calculation techniques to deal with nontrivial nonextensivity problems, we have recently extended [27,28] the Bogoliubov-Sadovnikov two-time GF framework [8,9] and the related SDM [9] to nonextensive classical statistical mechanics working conveniently within the so-called optimal Lagrangian multipliers (OLM) representation suggested in Ref. [29].…”

Section: Introductionmentioning

confidence: 99%

“…Two appendixes close the article. In Appendix A the recently proposed [27,28] two-time GF method in Tsallis classical statistical mechanics is shortly reviewed with the aim to point out the substantial differences between the nonextensive quantum and classical frameworks.…”

Section: Introductionmentioning

confidence: 99%

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Two-time Green’s functions and spectral density method in nonextensive quantum statistical mechanics

2008

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We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multipliers representation, the q-spectral properties and the methods for a direct calculation of the two-time q-Green's functions and the related q-spectral density (q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q = 1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q-induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q-induced nonextensivity close to the extensive regime are explicitly calculated in the lowtemperature regime by overcoming the calculation of the q grand-partition function.

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“…(27) and the sum rule (25), one can get another general result which, as in the extensive case, may play a relevant role in practical calculations involving the q GFs.…”

Section: Mechanicsmentioning

confidence: 88%

“…In classical nonextensive thermostatistics, the two-time q GFs involving two classical observables are defined by [27] …”

Section: Appendix A: Two-time Green's Functions and Spectral Den-sitymentioning

confidence: 99%

“…Actually, starting from the definitions of Poisson's brackets and q mean value, it can be shown that [27] …”

Section: Appendix A: Two-time Green's Functions and Spectral Den-sitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two-time Green’s functions and spectral density method in nonextensive quantum statistical mechanics

2008

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Thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet with long-range interactions via the spectral density method

Cavallo

Cosenza

Cesare

2004

Physica A: Statistical Mechanics and its Applications

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The thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet, with long-range interactions decaying as r −p and in the presence of an external magnetic field, is investigated by means of the spectral density method in the framework of classical statistical mechanics. We find that long-range order exists at finite temperature for d < p < 2d with d ≤ 2 and for p > d with d > 2, consistently with known theorems. Besides, the related critical temperature is determined and a study of the critical properties is performed.Recently, the critical properties at finite temperature of d-dimensional quantum Heisenberg models, with interactions of the type here considered (here often named "long-range spin models") have been studied using microscopic techniques [14,15,16,17] and Monte Carlo simulations [18]. A summary of the known features sounds as follows. The one-and two-dimensional long-range quantum spin-1/2 Heisenberg ferromagnets in absence of an external magnetic field were investigated by Nakano and Takahashi using the so called modified spin-wave theory [14] and the Schwinger-boson mean-field approximation [15]. Further information were derived for the d-dimensional case by means of the EMM for the two-time Green functions using the Tyablikov decoupling procedure [16]. Monte Carlo simulations for the two-dimensional quantum spin-1/2 Heisenberg model have been also performed for 2 < p ≤ 6 [18]. This scenario, has been recently enriched by an extension [17] of the Mermin-Wagner theorem [19] for the existence of ferromagnetic (FM) LRO at finite temperature in quantum Heisenberg and XY models in d(= 1, 2) dimensions with r −p -and oscillatory-interactions.Classical long-range spin-s Heisenberg FM models have attracted great atten-

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Spectral density approach to the one-dimensional classical Heisenberg ferromagnet with long-range interactions

2003

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Erratum: “Two-Time Green's Functions and the Spectral Density Method in Nonextensive Classical Statistical Mechanics”[Phys. Rev. Lett. 87, 240602 (2001)]

Cited by 6 publications

References 0 publications

Two-time Green’s functions and spectral density method in nonextensive quantum statistical mechanics

Two-time Green’s functions and spectral density method in nonextensive quantum statistical mechanics

Thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet with long-range interactions via the spectral density method

Spectral density approach to the one-dimensional classical Heisenberg ferromagnet with long-range interactions

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