The statistical mechanics of spin-1 Ising model with AFM/AFM interactions on a bilayer Bethe lattice

Albayrak, Erhan; Akkaya, Seyma; Cengiz, Tunç

doi:10.1016/j.jmmm.2009.07.034

Cited by 12 publications

(4 citation statements)

References 17 publications

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“…In equilibrium statistical physics, thin films have been investigated using Ising mechanics by various established theoretical methods e.g. mean-field theory (MFT) [12][13][14], spin-fluctuation theory [15], the effective field theory (EFT) [16,17], the series-expansion method [18], the exact recursion equation on the Bethe lattice [19], the cluster variation method in pair approximation [20], the renormalization-group (RG) method [21,22], and Monte Carlo (MC) simulations [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

A Monte Carlo study on the temperature dependence of hysteresis loops in Ising Spin-1 Square Bilayers

Chandra

2022

Preprint

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A Metropolis Monte Carlo simulation is used in this paper to investigate the temperature dependency of the hysteresis loops of a spin-1 bilayer with square monolayers. In this system, the atoms interact ferromagnetically in-plane, with either ferromagnetic or antiferromagnetic interplane interactions. The effects of four distinct combinations of the Hamiltonian parameters on the hysteresis behaviours are discussed in detail. The geometry of the hysteresis loops changes depending on how the exchange couplings are combined. With ferromagnetic interlayer coupling, only the central hysteresis loop opens while for the antiferromagnetic case, the hysteresis loop becomes a double loop for the specific combination of coupling strengths. Additionally, in all these cases, the area of the hysteresis loops grows with the gradual lowering of the temperature.

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Section: Introductionmentioning

confidence: 99%

A Monte Carlo study on the temperature dependence of hysteresis loops in Ising Spin-1 Square Bilayers

Chandra

2022

Preprint

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“…For being a sigle-spin model, such systems are, computationally and growth wise, less expensive than other ferrimagnetic models and belongs to the simplest of spin-systems for compensation. In literature, using Ising mechanics, layered systems have been studied by equilibrium Monte Carlo (MC) simulations in [25,26], by mean-field approximation (MFA) in [27], by effective-field approximation (EFA) in [28,29], by seriesexpansion method in [30], by renormalization-group (RG) method in [31], by spin-fluctuation theory in [32], by exact recursion equation on the Bethe lattice in [33] and by cluster variation method in pair approximation in [34].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic behaviour of magnetocaloric quantities in spin-1/2 Ising square trilayer

Chandra

2020

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We have studied a spin-1/2, Ising trilayered ferrimagnetic system on square Bravais lattice, employing Monte-Carlo simulation with single spin-flip Metropolis algorithm. The bulk of such a system is formed by three layers, each of which is composed completely either by A or B type of atoms, resulting in two distinct compositions: ABA and AAB and two different types of magnetic interactions: ferromagnetic between like atoms and antiferromagnetic between unlike atoms. Variation of relative interaction strengths in the Hamiltonian, for a range of values, leads to the shift of compensation point and critical point and changes in the magnitude of reduced residual magnetisation. We have tried to put forward probable mathematical forms of dependences of the reduced residual magnetisation and temperature interval between the compensation and critical points on controlling parameters in absence of applied magnetic field and have obtained phase diagrams for both types of configurations from these relations.

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“…Using Ising interactions, thin films have been studied in literature by computatinal and analytical techniques e.g. by equilibrium Monte Carlo (MC) simulations in [27,28], by mean-field theory (MFT) in [29], by effective-field theory (EFT) in [30,31,32,33], by series-expansion method in [34], by renormalizationgroup (RG) method in [35], by spin-fluctuation theory in [36], by exact recursion equation on the Bethe lattice in [37] and by pair approximation method (PAM) in [38,39]. Change in the underlying lattice structure may be significant since characterictics of any crystalline material depend on its lattice symmetry.…”

Section: Introductionmentioning

confidence: 99%

Compensation and its systematics in spin-1/2 Ising trilayered triangular ferrimagnet

Chandra

2020

Preprint

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We present a Monte Carlo study on a trilayered ferrimagnetic Ising system on triangular lattice, with s = 1/2 and three coupling constants. Three layers, making up the bulk, is formed completely by either A or B type of atoms. The interactions between like atoms (A-A; B-B) are ferromagnetic and between unlike ones (A-B) are anti-ferromagnetic. Two distinct trilayer compositions: AAB and ABA, are studied via Metropolis single spin flip algorithm and the location of the critical points (sublattice magnetisations vanish, leading to zero bulk magnetisation) and the compensation points (bulk magnetisation vanishes but nonzero sublattice magnetisations exist) are estimated and conditions for the existence of compensation points are determined. Close range simulations with variable lattice sizes for compensation point and Binder's cumulant crossing technique for critical points are employed for analysis. Comprehensive phase diagrams are obtained in the Hamiltonian parameter space and morphological studies at critical and compensation temperatures for both the configurations are also reported.

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The statistical mechanics of spin-1 Ising model with AFM/AFM interactions on a bilayer Bethe lattice

Cited by 12 publications

References 17 publications

A Monte Carlo study on the temperature dependence of hysteresis loops in Ising Spin-1 Square Bilayers

A Monte Carlo study on the temperature dependence of hysteresis loops in Ising Spin-1 Square Bilayers

Thermodynamic behaviour of magnetocaloric quantities in spin-1/2 Ising square trilayer

Compensation and its systematics in spin-1/2 Ising trilayered triangular ferrimagnet

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