Blume Emery Griffiths Model Research Articles

Critical and reentrant phenomena in the Blume–Emery–Griffiths model with attractive biquadratic interaction

Critical and reentrant phenomena in the Blume–Emery–Griffiths model with attractive biquadratic interaction

Monte Carlo and mean-field studies on the magnetic properties of a hexagonal Ising nanowire with core-shell structure in the Blume–Emery–Griffiths model

The mean-field approximation based on the Gibbs-Bogoliubov inequality and Monte Carlo simulations based on the Metropolis method in the Blume–Emery–Griffiths model were used to successfully examine a hexagonal Ising nanowire with spin-1. It was found that the model displays fascinating phase diagrams in various planes of interest by using both methods. The investigation of magnetic hysteresis cycles also exhibits interesting properties. The model not only presents first- and second-order phase transition lines, but also the tricritical and isolated critical points, multi-compensation temperatures, and magnetic hysteresis behavior with one to eight cycles.

Blume–Emery–Griffiths model for mixed spin (1, 5/2) calculated by mean-field approximation

Blume–Emery–Griffiths model for mixed spin (1, 5/2) calculated by mean-field approximation

The Blume–Emery–Griffiths Model on the FAD Point and on the AD Line

We analyse the Blume–Emery–Griffiths (BEG) model on the lattice Zd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}^d$$\\end{document} on the ferromagnetic-antiquadrupolar-disordered (FAD) point and on the antiquadrupolar-disordered (AD) line. In our analysis on the FAD point, we introduce a Gibbs sampler of the ground states at zero temperature, and we exploit it in two different ways: first, we perform via perfect sampling an empirical evaluation of the spontaneous magnetization at zero temperature, finding a non-zero value in d=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=3$$\\end{document} and a vanishing value in d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document}. Second, using a careful coupling with the Bernoulli site percolation model in d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document}, we prove rigorously that under imposing +\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$+$$\\end{document} boundary conditions, the magnetization in the center of a square box tends to zero in the thermodynamical limit and the two-point correlations decay exponentially. Also, using again a coupling argument, we show that there exists a unique zero-temperature infinite-volume Gibbs measure for the BEG. In our analysis of the AD line we restrict ourselves to d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document} and, by comparing the BEG model with a Bernoulli site percolation in a matching graph of Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}^2$$\\end{document}, we get a condition for the vanishing of the infinite-volume limit magnetization improving, for low temperatures, earlier results obtained via expansion techniques.

The microcanonical and the canonical phase diagrams of the mean-field Blume–Emery–Griffiths model

The microcanonical and the canonical phase diagrams of the mean-field Blume–Emery–Griffiths model

Critical and hysteresis behaviors for a hexagonal core-shell structure nanowire in the Blume–Emery–Griffiths model

The magnetic properties and hysteresis loops for the hexagonal Ising nanowire (HIN) with core–shell structure consisting of spin-32 are considered in the Blume–Emery–Griffiths (BEG) model by using the mean-field approximation (MFA) based on the Gibbs–Bogoliubov inequality for the free energy. The effects of various bilinear and biquadratic interaction parameters between the core, between the shell, and between the core and shell spins are considered for the phase diagrams of the model when temperature T=0 and T≠0 in addition to the crystal and external magnetic fields effects. The numerical calculations reveal that the model yields first- and second-order phase transition lines and tricritical points. In addition to the isolated critical and critical end-points, the model exhibits at most two compensation temperatures and interesting multiple hysteresis magnetic loops behaviors strongly dependent on the model parameters.

Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets

Critical end points and tricritical points are multicritical points that separate lines of continuous transitions from lines of first order transitions in the phase diagram of many systems. In models like the spin-1 disordered Blume–Capel model and the repulsive Blume–Emery–Griffiths model, the tricritical point splits into a critical end point and a bicritical end point with an increase in disorder and repulsive coupling strength respectively. In order to make a distinction between these two multicritical points, we investigate and contrast the behaviour of the first order phase boundary and the co-existence diameter around them.

Geometrical aspects of the multicritical phase diagrams for the Blume–Emery–Griffiths model

As a continuation of our preceding work [R. Erdem and N. Alata, Eur. Phys. J. Plus 135, 911 (2020), https://doi.org/10.1140/epjp/s13360-020-00934-3], we used the thermodynamic geometry in the Ruppeiner formalism to study the geometrical aspects of the multicritical phase diagrams for the spin-1 Blume-Emery- Griffiths model in the presence of crystal field. We derived an expression for the thermodynamic curvature or Ricci scalar (R) and analyzed its temperature and crystal field behaviours near interesting critical and multicritical points. Our findings are presented as geometrical phase diagrams including critical and multicritical topology. From these diagrams, new vanishing curvature lines (R = 0) extending into the ferromagnetic or paramagnetic phases beyond the critical points and zero point temperature are observed.

Gibbs Measures of the Blume–Emery–Griffiths Model on the Cayley Tree

Gibbs Measures of the Blume–Emery–Griffiths Model on the Cayley Tree

Blume–Emery–Griffiths model on random graphs

The Blume–Emery–Griffiths model with a random crystal field is studied in a random graph architecture, in which the average connectivity is a controllable parameter. The disordered average over the graph realizations is treated by replica symmetry formalism of order parameter functions. A self consistent equation for the distribution of local fields is derived, and numerically solved by a population dynamics algorithm. The results show that the average connectivity amounts to changes in the topology of the phase diagrams. Phase diagrams for representative values of the model parameters are compared with those obtained for fully connected mean field and renormalization group approaches.

Blume–Emery–Griffiths model for a magnetic bilayer. Magnetocaloric properties in the presence of the 1st-order phase transitions

In the paper the Blume–Emery–Griffiths model is studied for a magnetic bilayer with coordination number z=5. The Cluster Variational Method in Pair Approximation is employed. A special emphasis is put on the magnetic and magnetocaloric properties in the cases of the 1st order phase transitions. For such cases the magnetization, quadrupolar moment and magnetic entropy, as well as the isothermal entropy change and the adiabatic temperature change during demagnetization process are calculated. It is shown that in the vicinity of the temperature corresponding to the 1st order phase transitions the adiabatic demagnetization is not possible. Instead, the demagnetization process with the smallest entropy production is proposed.

Dynamic multicritical phase diagrams of the mixed spin (2, 5/2) Blume-Emery-Griffiths model with repulsive biquadratic coupling

We investigated the dynamic phase transitions (DPTs) in the mixed spin (2, 5/2) Blume-Emery Griffiths model with repulsive biquadratic interaction in the presence of a time-varying magnetic field. We used the path probability method to obtain the set of the dynamic equations. We numerically solved these dynamic equations to characterize the nature of first- and second-order phase transitions and to find the DPT temperatures as well as obtain the phases in the system. We constructed the dynamic phase diagrams (DPDs) in reduced temperature and amplitude of oscillating magnetic field plane. We observed that the DPDs display richer, complex and more topological various type of phase diagrams. In particular, DPDs exhibit the disordered phase, antiquadrupolar or staggered phase, six different ferrimagnetic phases, three different nonmagnetic phases, and numerous mixed phases. DPDs also display two dynamic tricritical points for only smaller values of crystal-field interactions, multiple critical end and double critical end points, one zero-temperature critical point, one inverse critical end point, and a quadruple point depending on interaction parameters. The system always shows the reentrant behaviors for the higher values of magnetic field amplitude, but it does not exhibit the dynamic tricritical behavior for higher values of crystal-field parameter.

Hysteretic dipolar and quadrupolar properties of the spin-1 Blume–Emery–Griffiths model under pair approximation

As a continuation of previously published work [A. Erdinç and M. Keskin, Int. J. Mod. Phys. B 18, 1603 (2004), doi:10.1142/S0217979204024823] the hysteretic properties of magnetization ([Formula: see text]) and quadrupolar moment ([Formula: see text] have been investigated for the spin-1 Blume–Emery–Griffiths model using pair approximation. The magnetic field ([Formula: see text]) dependence of [Formula: see text] is produced for different values of the lattice coordination number ([Formula: see text]), biquadratic interaction ([Formula: see text]) and single-ion anisotropy ([Formula: see text]). The ([Formula: see text]) loops show different and novelty properties when [Formula: see text]. We also observed the hysteresis cycles in the ([Formula: see text], ([Formula: see text] and ([Formula: see text]) planes. These curves strongly depend on biquadratic interaction [Formula: see text]. Our results are found to be in good agreement with the other theoretical findings.

Phase diagram of the repulsive Blume–Emery–Griffiths model in the presence of an external magnetic field on a complete graph

Using the repulsive Blume–Emery–Griffiths model, we compute the phase diagram in three field spaces, temperature (T), crystal field (Δ), and magnetic field (H) on a complete graph in the canonical and microcanonical ensembles. For low biquadratic interaction strengths (K), a tricritical point exists in the phase diagram where three critical lines meet. As K decreases below a threshold value (which is ensemble dependent), new multicritical points such as the critical end point and the bicritical end point arise in the (T, Δ) plane. For K > −1, we observe that the two critical lines in the H plane and the multicritical points are different in the two ensembles. At K = −1, the two critical lines in the H plane disappear, and as K decreases further, there is no phase transition in the H plane. At exactly K = −1, the two ensembles become equivalent. Beyond that, for all K < −1, there are no multicritical points, and there is no ensemble inequivalence in the phase diagram. We also study the transition lines in the H plane for positive K, i.e. for attractive biquadratic interaction. We find that the transition lines in the H plane are not monotonic in temperature for large positive values of K.

Magnetic-field induced multi-step transitions in ferromagnetic spin-crossover solids within the BEG model

We study by means of the 2D Blume–Emery–Griffiths (BEG) spin-1 model, spin-crossover (SCO) and prussian blue analogs (PBAs) solids. In this model, the spin states, which can be high-spin (HS) or low-spin (LS), interact magnetically and elastically with their nearest neighbors. To account for the volume change, accompanying the spin transition phenomenon, all interactions through the lattice are assumed as temperature-dependent. In addition, the system is subject to a variable magnetic field lifting the degeneracy in the HS state. A stochastic cooperative dynamics of this BEG-like Hamiltonian, describing the equilibrium and nonequilibrium properties of ferromagnetic spin-crossover solids, is derived from the Glauber approach, with appropriate Arrhenius microscopic transition rates. The model generates under the magnetic field, sigmoidal relaxation and a hysteresis phenomenon of the HS fraction, as well as multistep behavior of the magnetization. These behaviors open the way to new route of multi-stable systems, desired in multi-byte electronics.

Ruppeiner geometry of isotropic Blume–Emery–Griffiths model

With the aid of Ruppeiner thermodynamic metric defined on a two-dimensional phase space of dipolar (m) and quadrupolar (q) order parameters, we derive an expression for the Ricci scalar (R) in the isotropic Blume–Emery–Griffiths model. Temperature dependence of R is investigated for various values of bilinear to biquadratic ratio (r). Its behavior near the continuous/discontinuous phase transition temperatures and a tricritical point is presented. It is found that in addition to the divergence singularity and finite jumps connected with the phase transitions, there are field-dependent broad extrema in the Ricci scalar.

Absolute convergence of the free energy of the BEG model in the disordered region for all temperatures

We analyze the d-dimensional Blume–Emery–Griffiths model in the disordered region of parameters and we show that its free energy can be explicitly written in terms of a series which is absolutely convergent at any temperature in an unbounded portion of this region. As a byproduct we also obtain an upper bound for the number of d-dimensional fixed polycubes of size n.

Prediction of giant magnetocaloric effect in Ni40Co10Mn36Al14 Heusler alloys: An insight from ab initio and Monte Carlo calculations

In this work, based on limited experimental magnetocaloric data for Ni–Co–Mn–Al Heusler alloys, we present a theoretical study to predict a composition with higher magnetocaloric properties. By analogy with Ni–Co–Mn–(In, Sn) alloys exhibiting a large magnetization change across the structural transformation, we suppose that the addition of 10 at. % Co in Ni–Mn–Al would yield a similar trend. Our approach is based on the combination of ab initio calculations and Monte Carlo simulations within the framework of the Potts–Blume–Emery–Griffiths model. It follows from ab initio calculations that Co addition modifies the exchange interactions and enhances the ferromagnetism in austenite, while for martensite, the ferromagnetism is substantially suppressed due to the strongest antiferromagnetic Mn–Mn interactions. Thermo-magnetization curves and magnetocaloric properties under magnetic fields of 0.5 and 2 T are simulated by the Monte Carlo method assuming the ab initio exchange-interaction parameters. A large change in magnetization of approximately 100 A m2kg−1, leading to a giant magnetocaloric effect (ΔTad≈−7 K) across the martensite–austenite transformation, is predicted.

Reentrant phenomena of a mixed spin (5/2,3/2) Isotropic Blume–Emery–Griffiths model (BEG) on a graphene layer

Abstract Magnetic properties of a mixed spins (5/2,3/2) Isotropic Blume–Emery–Griffiths model (BEG) on a graphene layer have been studied within the framework of the Monte Carlo simulation. We have investigated the effects of the next nearest neighbors exchange interaction, the biquadratic exchange interaction and the longitudinal magnetic field on the critical and magnetic behaviors of the system. Interesting phenomena have been remarked. In particular, for appropriate parameters of the Hamiltonian, the system exhibits magnetization plateaus, double reentrant phenomena and compensation behavior.

Numerical simulations study of a spin-1 Blume–Emery–Griffiths model on a square lattice

We use the Monte Carlo simulation technique to study the critical behavior of a three-state spin model, with bilinear and biquadratic nearest-neighbor interactions, known as the Blume–Emery–Griffiths model (BEG), in a square lattice. In order to characterize this model, we study the phase diagram, in which we identify three different phases: ferromagnetic, paramagnetic and quadrupolar, the later with one sublattice filled with spins and the other with vacancies. We perform our studies by using two algorithms: Metropolis update (MU) and Wang–Landau (WL). The critical scaling behavior of the model is complementary studied by applying results obtained by using both algorithms, while tricritical points and the tricritical scaling behavior is analyzed by means of WL measuring the joint density of states and using the method of field mixing in conjunction with finite-size scaling. Furthermore, motivated by the decoupling between spins observed within the quadrupolar phase, we further generalize the BEG model in order to study the behavior of the system by adding a next nearest neighbour (NNN) interaction between spins. We found that by increasing the strength of the (ferromagnetic) NNN interaction, a new ferromagnetic phase takes over that contains both quadrupolar and ferromagnetic order.