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

Abstract

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-

Critical Temperature of Site-Diluted Spin-1/2 Systems with Long-Range Ferromagnetic Interactions

“…As far as the low-dimensional magnetism is concerned, we found that a non-zero critical temperature is found in all the systems where the interactions extend to infinity, provided n > d. This result is in accordance with theoretical predictions of several papers, for example: Quantum Monte Carlo method for 2D Heisenberg model, 33) spherical model in 1D Ising system, 2) one-and two-dimensional quantum Heisenberg model studied by spin wave theory, 34) Green Function technique 35) and Spectral Density method. 36) Another interesting limit of interaction considered in literature is n = 0, i.e., when the Author's version of the manuscript published in J. Phys. Soc.…”

Spectral density method in quantum nonextensive thermostatistics and magnetic systems with long-range interactions

“…In case of the Heisenberg model (15), the polar ansatz (19) yields reasonable results for the excitation spectrum and the relevant thermodynamic q-quantities in the low temperature regime. For describing other thermodynamic regimes in a wider range of temperatures, one could to adopt a new set of approximations involving additional decoupling procedures and higher order moment equations, consistently with the spirit of the SDM [4,5,6,7,8].…”

“…In this short note we have extended, in nonextensive quantum thermostatistics, the twotime GF formalism and the related SDM already developed for quantum [4,6] and classical [5,7,8] extensive systems. This offers the possibility to explore, at least in principle, the properties of realistic systems by using the big amount of experiences acquired in extensive problems.…”

“…There exists at present a large variety of methods and techniques for calculation of the GF's both in classical and quantum thermostatistics [1,2,3,4,5]. In particular, the related spectral density method (SDM), originally formulated by Kalashnikov and Fradkin [4] for quantum many-body systems, is a powerful nonperturbative tool which allows a direct study of the macroscopic properties of interacting quantum and classical many-body systems [4,5,6,7,8] also involving phase transitions.…”

Thermodynamics of the Classical Planar Ferromagnet Close to the Zero-Temperature Critical Point: A Many-Body Approach

“…In the present work, we will study the corresponding ddimensional classical XXZ spin model (CPFM) with particular attention to a field-induced quantum-like critical scenario for a direct comparison with the quantum counterpart. We will use the two-time Green's function method in classical statistical mechanics [29], developed and tested in [30][31][32][33], on microscopic classical spin model. This allows us to perform in parallel the quantum [28] and the classical analysis for any d, giving a transparent relation between the CPFM and the spin-S QPFM, both exhibiting a zerotemperature critical point.…”