Two-Time Green's Functions and the Spectral Density Method in Nonextensive Classical Statistical Mechanics

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

doi:10.1103/physrevlett.87.240602

Cited by 10 publications

(1 citation statement)

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“…These include the variational method [224][225][226], the Green-function methods [222,225,320,[330][331][332][333], the Darwin-Fowler steepest descent method [227,334], the Khinchin large-numbers-law method [229,335], and the counting in the microcanonical ensemble [230,231,336].…”

Section: Nonextensive Statistical Mechanics and Thermodynamicsmentioning

confidence: 99%

Introduction to Nonextensive Statistical Mechanics

Tsallis¹

2009

279

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Section: Nonextensive Statistical Mechanics and Thermodynamicsmentioning

confidence: 99%

Introduction to Nonextensive Statistical Mechanics

Tsallis¹

2009

279

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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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