APPLICATION OF THE GENETIC ALGORITHM TO BLUME–EMERY–GRIFFITHS MODEL: TEST CASES

2005 ◽  
Vol 19 (28) ◽  
pp. 4229-4237 ◽  
Author(s):  
OSMAN CANKO ◽  
MEHMET ŞAHİN ◽  
AHMET ERDİNÇ
Keyword(s):  
Genetic Algorithm ◽  
Mean Field ◽  
Stable State ◽  
Cluster Variation Method ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Variation Method ◽  
Simulation Techniques ◽  
Beg Model ◽  
Optimal Approach

The equilibrium properties of the Blume–Emery–Griffiths (BEG) model Hamiltonian with the arbitrary bilinear (J), biquadratic (K) and crystal field interaction (D) are studied using the genetic algorithm technique. Results are compared with lowest approximation of the cluster variation method (CVM), which is identical to the mean field approximation. We found the genetic algorithm to be very efficient for fast search at the average fraction of the spins, especially in the early stages as the system is far from the equilibrium state. A combination of the genetic algorithm followed by one of the well-tested simulation techniques seems to be an optimal approach. The curvature of the inverse magnetic susceptibility is also presented for the stable state of the BEG model.

The ferrimagnetic phase of the Blume-Emery-Griffiths model on the cellular automaton

Open Physics ◽  
2008 ◽  
Vol 6 (2) ◽  
Author(s):  
Nurgül Seferoğlu ◽  
Bülent Kutlu
Keyword(s):  
Phase Diagram ◽  
Cellular Automaton ◽  
Mean Field ◽  
Anisotropy Parameter ◽  
Cluster Variation Method ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Variation Method ◽  
Ferrimagnetic Phase ◽  
Creutz Cellular Automaton

AbstractThe Blume-Emery-Griffiths model is simulated using the cooling algorithm which is improved from the Creutz cellular automaton (CCA) under periodic boundary conditions. The simulations are carried out on a simple cubic lattice at K/J = −1.5 in the range of −3.5 < D/J < 0.5, with J and K representing the nearestneighbour bilinear and biquadratic interactions, D being the single-ion anisotropy parameter. The phase diagram characterizing phase transition of the model is obtained. We found different kinds of phase transitions between the ferromagnetic, quadrupolar, staggered quadrupolar and ferrimagnetic phases for K/J = −1.5. In particular, the region of the phase diagram containing a ferrimagnetic phase is explored and compared to those obtained by other methods. The simulations confirm that the ferrimagnetic phase occurs in the narrow interval −3.006 ≤ D/J < −3. This result is in a good agreement with Monte Carlo renormalization group and closer to the cluster variation method result than the mean field approximation result.

THE COUPLED SPIN-1 BLUME-CAPEL SUBLATTICES WITH DIFFERENT BILINEAR INTERACTIONS

2012 ◽  
Vol 26 (08) ◽  
pp. 1250042
Author(s):  
ERHAN ALBAYRAK ◽  
AHMET ERDINÇ
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Cluster Variation Method ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Variation Method ◽  
Crystal Fields ◽  
D Values

The equilibrium properties of the spin-1 Blume-Capel model are studied by the lowest approximation of the cluster-variation method which is identical to the mean-field approximation. The lattice is divided into two sublattices A and B, and different bilinear interaction parameters JAB and JBA between the nearest-neighbor spins are assumed. The temperature variations of the order-parameters are studied, therefore, the phase diagrams are obtained on the (JAB, T) planes for given values of JBA and crystal fields D. It was found that the model yields both second- and first-order phase transitions at higher positive D values and the lines of which combine at tricritical points. Negative values of D lead only second-order phase transitions. The phase diagrams are symmetric under the exchange of JAB with JBA as expected.

Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

2007 ◽  
Vol 62 (3-4) ◽  
pp. 127-139 ◽  
Author(s):  
M. Ali Pınar ◽  
Mustafa Keskin ◽  
Ahmet Erdinç ◽  
Osman Canko
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Mean Field ◽  
Cluster Variation Method ◽  
Field Approximation ◽  
Critical Behaviour ◽  
Mean Field Approximation ◽  
Variation Method ◽  
Cluster Variation

The critical behaviour of the ferromagnetic spin-3/2 Blume-Emery-Griffiths model with repulsive biquadratic coupling in the absence and presence of an external magnetic field is studied by using the lowest approximation of the cluster variation method, which is identical with the mean-field approximation. Thermal variations of the order parameters are investigated for different values of the interaction parameters and the external magnetic field. The complete phase diagrams of the system are calculated in the (kT/J,K/J), (kT/J,D/J) and (kT /J,H/J) planes. Five new phase diagram topologies are obtained, which are either absent from previous approaches or have gone unnoticed. A detailed discussion and comparison of the phase diagrams is made.

PHASE DIAGRAMS OF THE FCC BLUME–EMERY–GRIFFITHS MODEL ON A CELLULAR AUTOMATON

2007 ◽  
Vol 18 (09) ◽  
pp. 1417-1427 ◽  
Author(s):  
A. ÖZKAN ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Mean Field ◽  
State Diagram ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Face Centered Cubic ◽  
Face Centered ◽  
Creutz Cellular Automaton ◽  
Beg Model ◽  
Ferromagnetic Ordering

The spin-1 Ising (BEG) model has been simulated on a cellular automaton improved from the Creutz cellular automaton (CCA) for a face-centered cubic lattice. The simulations have been made in the 0 ≤ d = D/J ≤ 7 and -1.25 < k = K/J ≤ 0 parameter region. In this region, the ground state diagram (k, d) has ferromagnetic and perfect zero ordering regions. The ferromagnetic ordering region separates into four regions which exhibit different phase transition types as the first order, the second order, the reentrant, the double-reentrant and the successive phase transitions. The simulation results show that the model has the tricritical points, the critical end points and the bicritical points on the (kTC/zJ, d) and (kTC/zJ, k) planes as indicated by the Mean Field approximation results.

Modulated Phases on the FCC(110) Surfaces with Adsorbate-Induced Reconstructions

2003 ◽  
Vol 10 (02n03) ◽  
pp. 189-194
Author(s):  
Min Kang ◽  
Makoto Kaburagi
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Correlation Function ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Modulated Phases ◽  
The Mean ◽  
Beg Model

We theoretically investigate the fcc(110) surfaces with missing row reconstructions induced by adatoms using the Blume–Emmery–Griffith (BEG) model. In the model, Kij is introduced to denote interactions between surface atoms and Jij to describe interactions between dipoles. The investigation by the mean field approximation has predicted that there appear modulated phases on the surfaces as the next-nearest-neighbor (NNN) and the nearest-neighbor (NN) interactions along the [001] direction become competitive. In this study, Monte Carlo simulations are performed to confirm the prediction. A correlation function defined by concentration operators in wave vector q space is calculated. The results show that the concentration modulations appear. The temperature versus the ratio of the NNN interaction K2 to the NN interaction K1 phase diagram is obtained. The possible features of the modulated phases in experiments are discussed.

scholarly journals PHASE DIAGRAM OF ADSORBATE-INDUCED ROW-TYPE ALIGNMENTS

1999 ◽  
Vol 06 (05) ◽  
pp. 691-697 ◽  
Author(s):  
M. KANG ◽  
K. YASUTANI ◽  
M. KABURAGI
Keyword(s):  
Phase Diagram ◽  
High Temperatures ◽  
Nearest Neighbor ◽  
Chemical Potential ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Dipole Interactions ◽  
Beg Model ◽  
Incommensurate Phases

The phase diagram of adsorbate-induced row-type alignments, such as missing-row reconstructions induced by adsorbate atoms on the FCC(110) surface, is calculated by the Blume–Emmery–Griffiths (BEG) model. In the model, we introduce adatom–adatom and dipole–dipole interactions between nearest-neighbor (NN) and next-nearest-neighbor (NNN) rows. The calculation of the temperature versus adatom chemical potential phase diagram is performed using mean-field approximation. It is indicated that when NN and NNN interactions are competitive, there appear either dipole or coverage modulated (incommensurate) phases at high temperatures for a wide regime of the interactions.

The Determination of the Magnetoelectric Coupling Coefficient in Ferroelectric–Ferromagnetic Composite Based on PZT–Ferrite

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk
Keyword(s):  
Dielectric Permittivity ◽  
Coupling Coefficient ◽  
Mean Field ◽  
Field Approximation ◽  
Theoretical Description ◽  
Magnetoelectric Coupling ◽  
Mean Field Approximation ◽  
Dielectric Measurements ◽  
Temperature Dependences ◽  
Multiferroic Composite

Abstract In the present work, the magnetoelectric coupling coefficient, from the temperature dependences of the dielectric permittivity for the multiferroic composite was determined. The research material was ferroelectric-ferromagnetic composite on the based PZT and ferrite. We investigated the temperature dependences of the dielectric permittivity (") for the different frequency of measurement’s field. From the dielectric measurements we determined the temperature of phase transition from ferroelectric to paraelectric phase. For the theoretical description of the temperature dependence of the dielectric constant, the Hamiltonian of Alcantara, Gehring and Janssen was used. To investigate the dielectric properties of the multiferroic composite this Hamiltonian was expressed under the mean-field approximation. Based on dielectric measurements and theoretical considerations, the values of the magnetoelectric coupling coefficient were specified.

scholarly journals Hexagonal-Shaped Spin Crossover Nanoparticles Studied by Ising-Like Model Solved by Local Mean Field Approximation

2021 ◽  
Vol 7 (5) ◽  
pp. 69
Author(s):  
Catherine Cazelles ◽  
Jorge Linares ◽  
Mamadou Ndiaye ◽  
Pierre-Richard Dahoo ◽  
Kamel Boukheddaden
Keyword(s):  
Spin Crossover ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ligand Field ◽  
Order And Disorder ◽  
The Matrix ◽  
Local Mean ◽  
Parameter Values

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.

Geometrical and Transport Properties of Disordered Fibre Networks: Analytical Results

1997 ◽  
Vol 11 (20) ◽  
pp. 867-875 ◽  
Author(s):  
A. A. Rodríaguez ◽  
E. Medina
Keyword(s):  
Probability Distribution ◽  
Transport Properties ◽  
Geometrical Structure ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Fracture Networks ◽  
Simplified Models ◽  
Fibre Density ◽  
Line Network

We study novel geometrical and transport properties of a 2D model of disordered fibre networks. To assess the geometrical structure we determine, analytically, the probability distribution for the number of fibre intersections and resulting segment sizes in the network as a function of fibre density and length. We also determine, numerically, the probability distribution of pore perimeters and areas. We find a non-monotonous behavior of the perimeter distribution whose main features can be explained by solving for two simplified models of the line network. Finally we formulate a mean field approximation to conduction, above the percolation threshold, using the derived results. Relevance of the results to fracture networks will be discussed.

Sign in / Sign up

Export Citation Format

Share Document