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physica status solidi (b)

Phase Diagrams of the Mixed‐Spin XXZ Heisenberg Model on a Square‐Octagon Lattice

E. Dahbani, El Mostafa Jalal, N. Hachem, S. Zouhair, Karima El Kihel, M. El Bouziani

Published Sep 4, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1002/pssb.202500371

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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.
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.
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.
Quantum magnetic phase transition in square-octagon lattice was investigated by cellular dynamical mean field theory combining with continuous time quantum Monte Carlo algorithm. Based on the systematic calculation on the density of states, the double occupancy and the Fermi surface evolution of square-octagon lattice, we presented the phase diagrams of this splendid many particle system. The competition between the temperature and the on-site repulsive interaction in the isotropic square-octagon lattice has shown that both antiferromagnetic and paramagnetic order can be found not only in the metal phase, but also in the insulating phase. Antiferromagnetic metal phase disappeared in the phase diagram that consists of the anisotropic parameter λ and the on-site repulsive interaction U while the other phases still can be detected at T = 0.17. The results found in this work may contribute to understand well the properties of some consuming systems that have square-octagon structure, quasi square-octagon structure, such as ZnO.