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Romanian Journal of Physics

Critical Properties and Phase Transitions of the Mixed-Spin Anisotropic XXZ Heisenberg Model

El Mostafa Jalal, E. Dahbani, Hasnae Saadi, Ouafa Hachem, A. Hasnaoui, EL BOUZIANI M.

Published Mar 15, 2025• 4 citations
Publisher

Abstract

Using the Oguchi approximation, we have examined the magnetic properties of a mixed-spin (1/2, 1) XXZ Heisenberg model with a crystal field. The focus is on the 3D Heisenberg system, for which the phase diagrams and magnetizations are obtained numerically. It is found that the model features second- and first-order phase transition lines, as well as tricritical and critical end-points. The critical behavior is discussed and compared with previous works on Heisenberg systems.

DOI
10.59277/romjphys.2025.70.605

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Using the Oguchi approximation, we have examined the magnetic properties of a mixed-spin (1/2, 1) XXZ Heisenberg model with a crystal field. The focus is on the 3D Heisenberg system, for which the phase diagrams and magnetizations are obtained numerically. It is found that the model features second- and first-order phase transition lines, as well as tricritical and critical end-points. The critical behavior is discussed and compared with previous works on Heisenberg systems.
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.
This article investigates the magnetic properties and phase diagrams of a mixed spin‐1 and spin‐1/2 system on a 2D square‐octagon lattice within the quantum XXZ Heisenberg model using the Oguchi approximation. The sublattice magnetizations and total magnetization are analyzed as a function of temperature, providing insights into the thermal behavior of this mixed‐spin system. Additionally, the effect of the crystal field parameter on the magnetic properties is examined, revealing critical phenomena and phase transitions in the system. The influence of the anisotropy parameter is also explored, demonstrating its essential role in shaping the nature of the phase transitions and the emergence of tricritical behavior. The results contribute to a deeper understanding of the interplay between exchange interaction, crystal field, thermal fluctuations, and quantum effects in complex lattice systems.
A variational approach based on Bogoliubov inequality for the free energy is employed in order to treat the quantum spin-1 anisotropic ferromagnetic Heisenberg model in the presence of a crystal field. Within the Bogoliubov scheme an improved pair approximation has been used. The temperature-dependent thermodynamic functions have been obtained and provide much better results than the previous simple mean-field scheme. In one dimension, which is still nonintegrable for quantum spin-1, we get the exact results in the classical limit, or near-exact results in the quantum case, for the free energy, magnetization, and quadrupole moment, as well for the transition temperature. In two and three dimensions the corresponding global phase diagrams have been obtained as a function of the parameters of the Hamiltonian. First-order transition lines, second-order transition lines, tricritical and tetracritical points, and critical endpoints have been located through the analysis of the minimum of the Helmholtz free energy and a Landau-like expansion in the approximated free energy. Only first-order quantum transitions have been found at zero temperature. Limiting cases, such as isotropic Heisenberg, Blume-Capel, and Ising models, have been analyzed and compared to previous results obtained from other analytical approaches as well as from Monte Carlo simulations.
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.
Abstract The ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field interaction in the absence and presence of a longitudinal magnetic field on a three-dimensional cubic lattice is studied within the framework both of the mean-field approximation (MFA) and Monte Carlo simulation (MCS). Using the MFA, we have shown the phase diagram of the model for zero magnetic field in the (anisotropy, temperature) plane in which the system exhibits first- and second-order phase transitions and critical end-points. Also, we have used the standard MCS to confirm the previous results; we have presented the temperature dependence of the sublattice and total magnetizations for different values of anisotropy in order to determine the phase diagram of the model in the absence of a longitudinal magnetic field. In addition, the influence of this last field on the magnetic properties of the model is investigated and discussed.