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Revista Mexicana de Física

Monte Carlo studies of critical phenomena in mixed spin-3/2 and spin-5/2 Ising model on square lattice

N. De La Espriella, J. Madera Yancez, M. S. Páez Mesa

Published Jan 1, 2014• 7 citations
OpenAlex

Abstract

"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."

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"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."
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.
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.
To demonstrate the application of computational physics in modern statistical physics, this paper investigates the critical behavior of a finite-size ferromagnetic system based on the two-dimensional square-lattice Ising model.A nearest-neighbor Ising Hamiltonian is constructed, and periodic boundary conditions are adopted to reduce finite-boundary effects.The Metropolis Monte Carlo algorithm is used to sample spin configurations at different temperatures, while energy, magnetization, specific heat, magnetic susceptibility and Binder cumulant are calculated to describe the transition from an ordered state to a disordered state.The simulation results show that the system exhibits clear long-range order at low temperatures, where the order parameter remains high.As temperature increases, thermal fluctuations become stronger, magnetization decreases rapidly, and the system gradually evolves into a disordered state.The specific heat curve shows a pronounced peak at approximately (T = 2.269), while the susceptibility peak shifts slightly toward the high-temperature side due to finite-size effects and the discrete temperature grid.Overall, the simulated critical region is consistent with the theoretical critical temperature of the two-dimensional square-lattice Ising model.Spin-configuration analysis further reveals enhanced fluctuations and domain reconstruction near the critical region.In addition, a thermalization criterion and an extended sampling test for L = 48 near the critical region are added to examine the influence of finite sampling and equilibration.These results indicate that Monte Carlo simulation of the two-dimensional Ising model can effectively reproduce continuous phase transition, critical fluctuation and finite-size effects, providing a basic computational case for understanding critical phenomena in complex systems and data-driven physical analysis.
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 propose a new approach which permits us to obtain exact results for the mixed spin-1/2 and Spin- S ( S > 1/2) Ising models with single ion anisotropy Δ on the square lattice. We drive an explicit expression for the critical temperature for arbitrary values of S. We determine the exact phase diagrams for different values of S , and we show that there is no tricritical point. For S integer, there is no long range order when the anisotropy exceeds a critical value which is independent of S . Furthermore, the exact Ising transition temperature T C is always recovered, for any values of S, in the limit of Δ → − ∞ . These exact results are based on a conjecture which extend the analyticity of the n-spin-1/2 correlations functions (except at T = T C (Ising)) for any finite number n, to n → ∞ . This is confirmed by our calculations since our results are practically similar to those obtained by Monte Carlo simulations for S = 1, 2 and 3/2.
Purpose The authors investigate the magnetic properties of a mixed spin-3/2 and spin-2 Blume-Capel model on square and cubic lattices with two different single-ion anisotropies. Design/methodology/approach To study the critical behavior of a mixed spin-3/2 and spin-2 system, the authors have used a real space renormalization group approximation and specifically the Migdal-Kadanoff technique. The authors give the phase diagrams for two different cases: (1) on the (Δ/|J|, 1/|J|) plane with ΔA = ΔB = Δ, and (2) on the (ΔA/|J|, 1/|J|) and (ΔB/|J|, 1/|J|) planes for selected values of ΔB/|J| and ΔA/|J|, respectively. Findings The phase diagrams obtained show that the system exhibits both second- and first-order phase transitions as well as tricritical points for some values of the anisotropies. Moreover, using the variation of the free energy and its derivative at low temperatures, the authors have seen the appearance of first-order transitions at very low temperatures. Originality/value Few investigations of mixed spin-3/2 and spin-2 systems with crystal field have been realized. For this reason, the authors use the renormalization group approach to complete the work done on these systems. In absence of an exact solution, this contributes to the synthesis of the approximation results on mixed spins models.