The ising-heisenberg two-atom cluster approximation of a ferromagnet ()

Mielnicki, J.; Wiatrowski, G.; Balcerzak, T.

doi:10.1016/0304-8853(88)90084-4

Cited by 26 publications

(12 citation statements)

References 6 publications

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“…With using exact spin identities such as Callen-Suzuki identities [15,16] or generalization of them [17] we can calculate any observable of the system. Due to the avoid mathematical difficulties, the interaction between the cluster and outside of it treated within the Ising type interaction namely axial approximation [18]. To include Heisenberg character of the interaction to the formulation, minimum cluster size choice should be two.…”

Section: Model and Formulationmentioning

confidence: 99%

Magnetic properties of the multi-walled nanotubes constituted by localized magnetic moments: spin-1/2 case

Akıncı¹

2019

Preprint

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Magnetic properties of the multi-walled nanotubes have been investigated. Heisenberg model, which is a suitable model for the system consist of atoms with localized wave functions has been used. Effective field theory in two spin cluster for spin-1/2 has been numerically solved and critical properties such as phase diagrams as well as the behavior of the order parameter and hysteresis loops obtained.

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Section: Model and Formulationmentioning

confidence: 99%

Magnetic properties of the multi-walled nanotubes constituted by localized magnetic moments: spin-1/2 case

Akıncı¹

2019

Preprint

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“…In this approximation, we select two spins (namely s 1 and s 2 ) and treat the interactions exactly in this two spin cluster. In order to avoid some mathematical difficulties, we replace the perimeter spins of the two spin cluster by Ising spins (axial approximation) [32]. After all, by using the differential operator technique with decoupling approximation [29], we get an expression for the magnetization per spin as…”

Section: Model and Formulationmentioning

confidence: 99%

“…[30] (EFT-2 formulation). This EFT-2 formulation has been successfully applied to a variety of systems, such as quantum spin-1/2 Heisenberg ferromagnet [31,32] and antiferromagnet [33] systems, classical n-vector model [34,35], and spin-1 Heisenberg ferromagnet [36,37].…”

Section: Introductionmentioning

confidence: 99%

Random field effects on the anisotropic quantum Heisenberg model with Gaussian random magnetic field distribution

Akıncı

2013

Physica A: Statistical Mechanics and its Applications

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Effect of Gaussian random magnetic field distribution which is centered at zero on the phase transition properties of isotropic quantum Heisenberg model has been investigated on two (2D) and three dimensional (3D) lattices within the framework of effective field theory (EFT) for a two spin cluster (which is abbreviated as EFT-2). Beside the phase diagrams and the evolution of the magnetization versus temperature curves with the Gaussian magnetic field distribution width, critical Gaussian distribution width values, which make the critical temperature zero, have been obtained for several lattices. Moreover, it has been concluded that all critical temperatures are of the second order and reentrant behavior does not exist in the phase diagrams.Keywords: Quantum isotropic Heisenberg model; Random magnetic field; Gaussian magnetic distribution IntroductionRecently, there has been growing theoretical interest in the random field lattice spin models. The model was introduced for the first time by Larkin [1] for superconductors and later generalized by Imry and Ma [2]. Ising model which is the most basic lattice spin model with quenched random field (RFIM) has been studied over three decades, since this model can be used to describe a wide variety of disordered systems. Diluted antiferromagnets (such as F e x Zn 1−x F 2 , Rb 2 Co x M g 1−x F 4 and Co x Zn 1−x F 2 ) in a homogenous magnetic field behave like ferromagnetic systems in the presence of random fields [3,4]. Structural phase transitions in random alloys, commensurate chargedensity-wave systems with impurity pinning, binary fluid mixtures in random porous media, and the melting of intercalates in layered compounds, such as T iS 2 [5] are the examples of the experimentally accessible disordered systems which can be described by RFIM. Besides, RFIM can mimic the phase transitions and interfaces in random media [6,7], e.g pre-wetting transition on a disordered substrate can be mapped onto a 2D RFIM problem [8]. RFIM has also been applied to describe critical surface behavior of amorphous semi-infinite systems [9,10].RFIM has been widely studied in the literature with discrete [11,12,13,14,15], as well as continous [16,17,18,19,20,21] distributions. Random distribution of the magnetic field may produce drastic effects on the phase diagrams and related magnetic properties of the system. It has been shown that Ising systems under the influence of discrete symmetric distributions, like bimodal [11] and trimodal [12] distributions, exhibit tricritical behavior, while continuous symmetric distributions like Gaussian distribution [16] lead to only second order transitions.Although the results of the RFIM have been reported for both discrete and continuous distributions, there has been less attention paid on the random field effects on the Heisenberg model. Since Heisenberg model is more realistic model than the Ising model for the spin systems, it is important to investigate this model in the presence of quenched random fields. Albuquerque and Arruda [22] studi...

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“…[20] (namely EFT-2 formulation). This EFT-2 formulation has been successfully applied to a variety of systems, such as quantum S-1/2 Heisenberg ferromagnet [21,22] and antiferromagnet [23] systems, classical n-vector model [24,25], and spin-1 Heisenberg ferromagnet [26,27].…”

Section: Introductionmentioning

confidence: 99%

Bond diluted anisotropic quantum Heisenberg model

Akıncı

2013

Journal of Magnetism and Magnetic Materials

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Effects of the bond dilution on the critical temperatures, phase diagrams and the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg model have been investigated in detail. For the isotropic case, bond percolation threshold values have been determined for several numbers of two (2D) and three (3D) dimensional lattices. In order to investigate the effect of the anisotropy in the exchange interaction on the results obtained for the isotropic model, a detailed investigation has been made on a honeycomb lattice. Some interesting results, such as second order reentrant phenomena in the phase diagrams have been found. Keywords: Quantum anisotropic Heisenberg model; bond dilution; bond percolation threshold IntroductionQuenched randomness effects are very important in modeling real materials, since consideration of these effects simulates a realistic model of real materials. Real materials have some uncontrollable defects and these defects can be modeled by introducing site dilution (randomly distributed non magnetic atoms), bond dilution (randomly broken bonds between the magnetic atoms) or both of them into the related model. It is a well known fact that, Heisenberg model produces more realistic results than the Ising model, in order to explain the magnetic properties of real materials. Thus, it is important to work on the Heisenberg model with these quenched randomness effects. These quenched randomness effects produce different behaviors in the magnetic properties of the model, e.g. different phase transition characteristics from the pure model (i.e. the model without any quenched randomness effects).Heisenberg model with quenched randomness effects has been studied widely by a variety of methods, such as spin-1/2 (S-1/2) isotropic Heisenberg model with bond dilution on 2D lattices with Monte Carlo (MC) simulation [1,2,3,4], anisotropic model (by means of the XXZ model) on 2D lattices with real space renormalization group (RSRG) technique [5]. On the other hand, random bond distributed systems in which spin glass phases originate have been studied, e.g. discrete distribution on S-1/2 Heisenberg model with pair approximation [6,7], density matrix product approximation [8], Gaussian distribution with imaginary time Grassmann field theory [9] and S-1 Heisenberg model with discretely distributed random bonds with exact diagonalization method [10]. Besides, both site and bond diluted systems have been studied with quantum MC on 2D lattices [11] and S-1/2 Heisenberg model with site-bond correlated dilution (which covers uncorrelated site dilution as a limit) on 2D and 3D lattices with RSRG [12] and MC [13], and also using a variational principle for the free energy [14]. All of these work are related to the isotropic Heisenberg model or XXZ model.The aim of this work is determine the effect of the bond dilution on the phase diagrams and the thermodynamic properties of the anisotropic quantum Heisenberg model. By anisotropy, we do not restrict ourselves with XXZ model. Namely, we want to d...

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The ising-heisenberg two-atom cluster approximation of a ferromagnet ()

Cited by 26 publications

References 6 publications

Magnetic properties of the multi-walled nanotubes constituted by localized magnetic moments: spin-1/2 case

Magnetic properties of the multi-walled nanotubes constituted by localized magnetic moments: spin-1/2 case

Random field effects on the anisotropic quantum Heisenberg model with Gaussian random magnetic field distribution

Bond diluted anisotropic quantum Heisenberg model

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