Papers by Smaine Bekhechi
Chinese Journal of Physics, 2021
Computational Condensed Matter, 2018
Physics Letters A, 2021
Abstract The effects of RKKY interaction and the influence of the four spin interaction J 4 , on ... more Abstract The effects of RKKY interaction and the influence of the four spin interaction J 4 , on the multi-layer transition and magnetic properties of a spin-1/2 Ashkin Teller model of a ferromagnetic system shaped by two magnetic multi-layer materials, of different thicknesses, separated by a non-magnetic spacer of thickness M, are examined using Monte Carlo simulations. The system presents a new partially ordered phase σ S > , for various values of J 4 / J 2 , and exhibits behavior typical of a second-order phase transition. It is found that the transition temperatures of the two blocks are strongly dependent on the thickness of the magnetic layers N and the four-spin coupling J 4 / J 2 , while they do not depend on the non-magnetic spacer and the Fermi level k f . Finally, We have obtained a critical thickness M L of the non-magnetic spacer above which the multi-layer blocks undergo a transition separately at different temperatures, for J 4 / J 2 = 3 and k f = 0.2 .
Physical Review B, 1999
Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo s... more Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-Teller model ͑ATM͒. We have obtained rich phase diagrams with first-and second-order phase transitions with several multicritical points of higher order. Also this model exhibits a partially ordered phase PO 2 which does not exist in the spin-1/2 Ashkin-Teller model ͑ATM͒. Finally, the critical behavior of this model is discussed. ͓S0163-1829͑99͒00609-8͔
Physical Review E, 2001
We study a two-dimensional nonequilibrium Ashkin-Teller model based on competing dynamics induced... more We study a two-dimensional nonequilibrium Ashkin-Teller model based on competing dynamics induced by contact with a heat bath at temperature T, and subject to an external source of energy. The dynamics of the system is simulated by two competing stochastic processes: a Glauber dynamics with probability p, which simulates the contact with the heat bath; and a Kawasaki dynamics with probability 1Ϫp, which takes into account the flux of energy into the system. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. The phase diagrams of the model exhibit a self-organization phenomenon for certain values of the fourth coupling interaction strength. On the other hand, from exponent calculations, the equilibrium critical behavior is preserved when nonequilibrium conditions are applied.
Central European Journal of Physics, 2014
An open ferromagnetic Ashkin-Teller model with spin variables 0, ±1 is studied by standard Monte ... more An open ferromagnetic Ashkin-Teller model with spin variables 0, ±1 is studied by standard Monte Carlo simulations on a square lattice in the presence of competing Glauber and Kawasaki dynamics. The Kawasaki dynamics simulates spin-exchange processes that continuously flow energy into the system from an external source. Our calculations reveal the presence, in the model, of tricritical points where first order and second order transition lines meet. Beyond that, several self-organized phases are detected when Kawasaki dynamics become dominant. Phase diagrams that comprise phase boundaries and stationary states have been determined in the model parameters’ space. In the case where spin-phonon interactions are incorporated in the model Hamiltonian, numerical results indicate that the paramagnetic phase is stabilized and almost all of the self-organized phases are destroyed.
Physical Review B, 2000
In a three dimensional lattice, another term of the energy is adjusted on the Shnidman-Zia model ... more In a three dimensional lattice, another term of the energy is adjusted on the Shnidman-Zia model in order to obtain the lamellar phase. Phase behaviours of the new Hamiltonian are determined using the perturbation theory and the mean field analysis. We investigate the phase diagrams in (T, S) and (T, p a) planes. The phase diagrams exhibit a rich variety of behaviour: second order, first order and multicritical points. We find that the lamellar phase appears for certain values of the parameters of the system. Moreover, other new phases are obtained which correspond to physical micellar phases.
Physical Review B, 2000
Two nonperturbative methods such as transfer-matrix finite-size scaling and Monte Carlo simulatio... more Two nonperturbative methods such as transfer-matrix finite-size scaling and Monte Carlo simulations are used to investigate the multicritical behavior of a lattice-gas model proposed by Shnidman and Zia ͓J. Stat. Phys 50, 839 ͑1988͔͒ for studying the micellar binary solutions of water and amphiphile. The phase diagrams are obtained in both the magnetic field-temperature ͑H,T͒ and amphiphile density temperature (s ,T) for different values of competing interactions (K 0 and K 1) and in the presence of the attraction interaction intermicellar parameter ͑J͒. Our nonperturbative results are compared with previous mean-field ones. Both methods confirm the absence of the rarefied micelle at high temperature as found previously by mean-field calculations. Also our phase diagrams present transitions of first-and second-order transitions linked by tricritical and multicritical points of higher order. Finally, with the use of finite-size-scaling ideas, the critical exponents have been calculated. Our results show that this model has a nonuniversal behavior that belongs to the XY model with cubic anisotropy for a certain range of interactions parameters and a universal behavior that belongs to the dϭ2 Ising model.
Physica A: Statistical Mechanics and its Applications, 2003
The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Car... more The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Carlo method based on Wolff cluster algorithm. With varying the surface coupling, js=Js/J, the phase diagram exhibits a special surface coupling jsp at which all the films have a unique critical temperature Tc for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two- to three-dimensional behavior are found at this point.
Journal of Magnetism and Magnetic Materials, 2020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A two dimensional antiferromagnetic spin-1 Ising model with negative next-nearest neighbour inter... more A two dimensional antiferromagnetic spin-1 Ising model with negative next-nearest neighbour interaction (J2 < 0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis.
Physical Review E, 2001
We study a two-dimensional nonequilibrium Ashkin-Teller model based on competing dynamics induced... more We study a two-dimensional nonequilibrium Ashkin-Teller model based on competing dynamics induced by contact with a heat bath at temperature T, and subject to an external source of energy. The dynamics of the system is simulated by two competing stochastic processes: a Glauber dynamics with probability p, which simulates the contact with the heat bath; and a Kawasaki dynamics with probability 1Ϫp, which takes into account the flux of energy into the system. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. The phase diagrams of the model exhibit a self-organization phenomenon for certain values of the fourth coupling interaction strength. On the other hand, from exponent calculations, the equilibrium critical behavior is preserved when nonequilibrium conditions are applied.
Physical Review B, 1999
Two non perturbative methods by means of the Transfer-Matrix Finite-Size-Scaling (TMFSS) and Mont... more Two non perturbative methods by means of the Transfer-Matrix Finite-Size-Scaling (TMFSS) and Monte-Carlo (MC) simulations are used to investigate the spin-1 Ashkin-Teller model (A.T.M). We have obtained rich phase diagrams with first and second order phase transitions with several multicritical points of higher order. Also this model exhibits a new partially ordered phase PO2 which does not exist in the spin-1/2 Ashkin-Teller model (A.T.M). Finally, the critical behaviour of this model is discussed.
We have investigated numerically a statistical model of four component systems, which exhibit two... more We have investigated numerically a statistical model of four component systems, which exhibit two critical temperatures, called the Ashkin-Teller model (ATM). The effects of, the anisotropy coupling, the single ion potential field and the mixed spin on the structure of the phase diagram have been studied. The model presents a rich variety of phase transitions which meet on tricritical or multicritical points. Different partially ordered phases with a partially broken symmetry appears at high temperatures. Their region of stability and their structure depend on the phase parameter space. The nature of critical lines which bound these partially ordered phases depends on the coupling parameters and the cristalline anisotripy".
Transfer-matrix finite-size-scaling calculations and Monte Carlo simulations are used to investig... more Transfer-matrix finite-size-scaling calculations and Monte Carlo simulations are used to investigate the two-dimensional spin-3/2 Ising antiferromagnet in the presence of an external magnetic field and a single-ion potential. Comparison is made between the results of this study and previous mean-field calculations. The phase diagrams and the critical behavior of the model are discussed. In contrast to the mean-field picture, no decomposition of the tricritical point is observed. S0163-18299700845-X
The critical surface phenomena of a magnetic thin Ising ÿlm is studied using numerical Monte-Carl... more The critical surface phenomena of a magnetic thin Ising ÿlm is studied using numerical Monte-Carlo method based on Woll cluster algorithm. With varying the surface coupling, js = Js=J , the phase diagram exhibits a special surface coupling jsp at which all the ÿlms have a unique critical temperature Tc for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two-to three-dimensional behavior are found at this point.
In a three-dimensional lattice, another term of the energy is adjusted on the Shnidman-Zia model ... more In a three-dimensional lattice, another term of the energy is adjusted on the Shnidman-Zia model in order to obtain the lamellar phase. Phase behaviors of the new Hamiltonian are determined using the perturbation theory and the mean-field analysis. We investigate the phase diagrams in (T,) and (T, a) planes. The phase diagrams exhibit a rich variety of behavior: second-order, first-order, and multicritical points. We find that the lamellar phase appears for certain values of the parameters of the system. Moreover, other new phases are obtained that correspond to physical micellar phases.
Two nonperturbative methods such as transfer-matrix finite-size scaling and Monte Carlo simulatio... more Two nonperturbative methods such as transfer-matrix finite-size scaling and Monte Carlo simulations are used to investigate the multicritical behavior of a lattice-gas model proposed by Shnidman and Zia J. Stat. Phys 50, 839 1988 for studying the micellar binary solutions of water and amphiphile. The phase diagrams are obtained in both the magnetic field-temperature H,T and amphiphile density temperature (s ,T) for different values of competing interactions (K 0 and K 1) and in the presence of the attraction interaction intermicellar parameter J. Our nonperturbative results are compared with previous mean-field ones. Both methods confirm the absence of the rarefied micelle at high temperature as found previously by mean-field calculations. Also our phase diagrams present transitions of first-and second-order transitions linked by tri-critical and multicritical points of higher order. Finally, with the use of finite-size-scaling ideas, the critical exponents have been calculated. Our results show that this model has a nonuniversal behavior that belongs to the XY model with cubic anisotropy for a certain range of interactions parameters and a universal behavior that belongs to the d2 Ising model.
An open ferromagnetic Ashkin-Teller model with spin variables 0 ±1 is studied by standard Monte C... more An open ferromagnetic Ashkin-Teller model with spin variables 0 ±1 is studied by standard Monte Carlo simulations on a square lattice in the presence of competing Glauber and Kawasaki dynamics. The Kawasaki dynamics simulates spin-exchange processes that continuously flow energy into the system from an external source. Our calculations reveal the presence, in the model, of tricritical points where first order and second order transition lines meet. Beyond that, several self-organized phases are detected when Kawasaki dynamics become dominant. Phase diagrams that comprise phase boundaries and stationary states have been determined in the model parameters' space. In the case where spin-phonon interactions are incorporated in the model Hamiltonian, numerical results indicate that the paramagnetic phase is stabilized and almost all of the self-organized phases are destroyed.
Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo s... more Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-Teller model ATM. We have obtained rich phase diagrams with first-and second-order phase transitions with several multicritical points of higher order. Also this model exhibits a partially ordered phase PO 2 which does not exist in the spin-1/2 Ashkin-Teller model ATM. Finally, the critical behavior of this model is discussed. S0163-18299900609-8
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Papers by Smaine Bekhechi