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Critical and hysteresis phenomena in the mixed spin-(32, 12) anisotropic two-dimensional Heisenberg model: A Monte Carlo study

Seto, G., Yessoufou, R.A.A., Kpadonou, A., Albayrak, E.

Published Jan 1, 2022• 0 citations
OpenAlex

Abstract

The critical and hysteresis behaviors of the ferromagnetic mixed-spin system consisting of two sublattices A and B with two types of spins SA=32 and SB=12 described by anisotropic Classical-Heisenberg Model on a square lattice are examined by using Monte Carlo simulations based on metropolis algorithm. By exploiting the thermal variations of the order-parameters and the magnetic susceptibility, the phase diagrams are calculated on the (Dz/J, kBT/J), (Dx/J, kBT/J) and (Δ, kBT/J) planes and the effects of various interaction parameters in the Hamiltonian are explored. It is found that the model yields only second-order phase transitions. We have also estimated the critical exponents ν, β and γ of the model as functions of Dz and Dx by using the finite-size scaling arguments and found that they depend on the details of the model. Finally, the hysteresis behavior of the model is also investigated and it is revealed that the width of hysteresis loop decreases with temperature while it increases for positive Dz values.

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Ground-state properties of the two-dimensional S =1/2 Heisenberg Mattis model is investigated using the world-line quantum Monte Carlo method. Calculations of the spin glass order parameter show that the term proportional to L -2 is dominant in the scaling of this order parameter, and that this order parameter increases monotonously as the concentration of ferromagnetic bonds, p , is enhanced. Simulations of the Néel order parameter and the staggered susceptibility show that the Néel-Mattis spin glass phase boundary of the present model is consistent with the critical concentration of the two-dimensional Ising Mattis model, p c ≃0.147, and that the critical exponents of these quantities are β/ν=0.32±0.05 and γ/ν=1.86±0.15, respectively. These estimates result in a nontrivial dynamical critical exponent, z =0.50±0.25.

Journal of the Physical Society of Japan•Sep 15, 1997•0 citations
The critical and hysteresis behaviors of the ferromagnetic mixed-spin system consisting of two sublattices A and B with two types of spins SA=32 and SB=12 described by anisotropic Classical-Heisenberg Model on a square lattice are examined by using Monte Carlo simulations based on metropolis algorithm. By exploiting the thermal variations of the order-parameters and the magnetic susceptibility, the phase diagrams are calculated on the (Dz/J, kBT/J), (Dx/J, kBT/J) and (Δ, kBT/J) planes and the effects of various interaction parameters in the Hamiltonian are explored. It is found that the model yields only second-order phase transitions. We have also estimated the critical exponents ν, β and γ of the model as functions of Dz and Dx by using the finite-size scaling arguments and found that they depend on the details of the model. Finally, the hysteresis behavior of the model is also investigated and it is revealed that the width of hysteresis loop decreases with temperature while it increases for positive Dz values.
"We used a Monte Carlo simulation to analize the magnetic behavior of Ising model of mixed spins S A i = ß3=2 ; ß1=2 and æ B j = ß 5 = 2 ; ß 3 = 2 ; ß 1 = 2 , on a square lattice. Were studied the possible critical phenomena that may emerge in the region around the multiphase point (D= j J 1 j = ° 3 ;J 2 = j J 1 j = 1) and the dependence of the phase diagrams with the intensities of the anisotropy field of single ion (D= j J 1 j ) and the ferromagnetic coupling of exchange spin S A i (J 2 = j J 1 j). The system displays first order phase transitions in a certain range of the parameters of the Hamiltonian, which depend on D= j J 1 j and j J 2 = j J 1 j . In the plane (D= j J 1 j ;k B T= j J 1 j), the de- crease of j D= j J 1 jj , implies that the critical temperature, T c , increases and the first order transition temperature, T t , decreases. In the plane (J2 = j J 1 j ;k B T= j J 1 j ), T c increases with the increasing of J 2 = j J 1 j , while that T t decreases."
The critical behavior of 2D magnetic easy-plane systems has mainly been studied by the classical XY model. However, the z components of the spins have to be considered in order to describe real systems, and their fluctuations cannot positively be neglected when quantum effects are to be included, quantum spins being intrinsically three-component objects. Therefore, Monte Carlo simulations are performed for the Heisenberg ferromagnet with easy-plane anisotropy (XXZ model) on a two-dimensional square lattice with a twofold aim: first, to obtain accurate quantitative results about the critical behavior of the classical model, showing the relevant role played by the out-of-plane fluctuations; second, to open the way for approaching the quantum thermodynamics by means of the effective Hamiltonian method that reduces the quantum thermodynamics of the XXZ ferromagnet to the investigation of an effective classical model with temperature-dependent renormalized interaction parameters. Specific heat, magnetic susceptibility, and correlation length are calculated in the critical region for lattice sizes up to 128×128. These quantities preserve the Kosterlitz–Thouless behavior of the XY model. For the transition temperature of the classical XX0 model we obtain the estimate kBTc/(JS̃2)=0.69±0.01.
The mixed spin-7/2 and spin-1/2 Ising model with a crystal field in the absence and presence of an external longitudinal magnetic field is investigated within the framework both of the renormalization group (RG) method and Monte Carlo simulation (MCS). First, we have determined the ground-state phase diagram. Then, using RG technique, the finite temperature phase diagrams of this model are plotted for the two- and three-dimensional cases by following the flow in the parameters space of the Hamiltonian and evaluating the free energy and its isotherm derivative at low temperatures. Our results show that the model exhibits first- and second-order phase transitions as well as critical end-points. In addition, by linearizing the RG transformation at the vicinity of the fixed points of the second-order transition, we have determined the critical exponents. The MCS is also employed to validate the results obtained previously by renormalization, and to examine the influence of an external magnetic field on the magnetic properties and hysteresis loops of the system.
We have employed the Oguchi approximation (OA) to investigate the effects of a random crystal field which is active (inactive) with probability [Formula: see text] [Formula: see text] for given lattice sites on the thermodynamic properties of the mixed spin-[Formula: see text] anisotropic Heisenberg model in the presence of an external magnetic field. By exploiting the thermal variations of the order parameters, interesting phase diagrams are produced on various planes. The phase diagrams show first- and second-order transition lines and also tricritical points. In addition to the reentrant behavior which is localized in a certain range of [Formula: see text] at very low temperature, the magnetic exponent [Formula: see text] calculated near the critical point exhibits interesting behaviors depending on the crystal field interaction. The hysteresis behavior of the model is also investigated and it reveals that the width of hysteresis loop decreases or increases, respectively, for negative or positive crystal field region as the probability [Formula: see text] increases.
Using the Monte Carlo Simulation (MCS) method combined with the Metropolis algorithm, we explore the magnetic properties of a two-dimensional (2D) spin system with spins 1, 2 and 3. The adapted simulation to the Ising model aims to study the impact of the correction term a of the interaction with second neighbors and the crystal field D on the critical temperature [Formula: see text] of the 2D anisotropic square lattice for different integer values of spins. The obtained results demonstrate that the critical temperature [Formula: see text] is significantly affected by the competing interactions between the anisotropy parameter, second-neighbor interaction and the crystal field. The considered model exhibits a critical phase transition regardless of the spin S value where the critical temperature increases with the value of S. Note that this phase transition occurs under the condition [Formula: see text]. Moreover, the obtained results show that the complex interactions give rise to a variety of phase diagrams, thereby revealing the richness of possible magnetic behaviors in the studied system.
Ground-state properties of the two-dimensional S =1/2 Heisenberg Mattis model is investigated using the world-line quantum Monte Carlo method. Calculations of the spin glass order parameter show that the term proportional to L -2 is dominant in the scaling of this order parameter, and that this order parameter increases monotonously as the concentration of ferromagnetic bonds, p , is enhanced. Simulations of the Néel order parameter and the staggered susceptibility show that the Néel-Mattis spin glass phase boundary of the present model is consistent with the critical concentration of the two-dimensional Ising Mattis model, p c ≃0.147, and that the critical exponents of these quantities are β/ν=0.32±0.05 and γ/ν=1.86±0.15, respectively. These estimates result in a nontrivial dynamical critical exponent, z =0.50±0.25.