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Effects of bimodal random crystal field on the phase transition of mixed spin-1/2 and spin-1 on nanotube

LI Xiao-jie, WANG Miao-Miao, CHEN Wen-Long, Fei Gao, ZHANG Meng, Chong wang

Published Jan 1, 2024• 0 citations
OpenAlex

Abstract

The magnetization and phase transition of mixed spin-1/2 and spin-1 Blume-Capel model on a cylindrical Ising nanotube with bimodal random crystal fields were investigated by using the effective field theory. Employing numerical calculation, the phase diagrams and the magnetization which depends on the temperature and the parameters of random crystal fields were obtained. The results show that：(1) Changing the probability and the ratio of the crystal fields, bimodal random crystal fields may describe different doped atoms acting on spins. (2) The critical points do exist for certain values of the probability, the negative or positive crystal field and the ratio of the crystal fields. (3) The system shows several phase transition temperatures, first-order and second-order phase transitions.

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The magnetization and phase transition of mixed spin-1/2 and spin-1 Blume-Capel model on a cylindrical Ising nanotube with bimodal random crystal fields were investigated by using the effective field theory. Employing numerical calculation, the phase diagrams and the magnetization which depends on the temperature and the parameters of random crystal fields were obtained. The results show that：(1) Changing the probability and the ratio of the crystal fields, bimodal random crystal fields may describe different doped atoms acting on spins. (2) The critical points do exist for certain values of the probability, the negative or positive crystal field and the ratio of the crystal fields. (3) The system shows several phase transition temperatures, first-order and second-order phase transitions.
The magnetic and thermodynamic properties of the Blume-Capel model are investigated within an approach combined with quantum mechanics and mean-field approximation for the spin-1/2 and spin-1 with coordination number z = 3. The spin-1 sites are subjected to transverse crystal fields Dx and Dy. In addition, the bilinear interaction parameter J is randomly distributed with an adjustable parameter α>0 such that certain sites are under the influence of αJ with probability p while the rest are subject to J with probability 1−p. The thermal behaviors of the order parameters have been studied to determine the nature of phase transitions and to calculate phase diagrams in the (Dx,kT), (Dy,kT), (α,kT), (|J|,kT), and (p,kT) planes. The obtained results revealed a rich variety of critical phenomena including first- and second-order phase transitions, tricritical points, and compensation temperatures. Under an external magnetic field, the system exhibits both simple and multi-hysteresis behaviors. Furthermore, the coercive field and remanent magnetization decrease with increasing temperature.
The bimodal random crystal field(?) effects are investigated on the phase diagrams of spin-3/2 Ising model by using the effective-field theory with correlations based on two approximations:the general van der Waerden identity and the approximated van der Waerden identity.In our approach,the crystal field is either turned on or turned off randomly for a given probability p or q = 1- p,respectively.Then the phase diagrams are constructed on the(?,kT /J) and(p,kT /J)planes for given p and ?,respectively,when the coordination number is z = 3.Furthermore,the effect of randomization of the crystal field is illustrated on the(?,kT /J) plane for p = 0.5 when z = 3,4,and 6.All these are carried out for both approximations and then the results are compared to point out the differences.In addition to the lines of second-order phase transitions,the model also exhibits first-order phase transitions and the lines of which terminate at the isolated critical points for high p values.
In this work, we investigate the thermodynamic properties of the quantum Blume-Capel model with spin S=5/2 S = 5/2 S=5/2 in the presence of transverse and random crystalline fields. The system is described by a Hamiltonian that includes ferromagnetic exchange interactions between nearest neighbors, a longitudinal single-ion anisotropy, and a transverse single-ion anisotropy. Using a mean-field approach based on Bogoliubov's inequality for the Gibbs free energy, we derive the fundamental thermodynamic potential and the equation of state for the magnetization. The influence of the longitudinal and transverse anisotropy parameters on the magnetic ordering and phase transitions is analyzed in detail. We present magnetization versus temperature diagrams for various combinations of the anisotropies, exploring both positive and negative values. Our results reveal that the system exhibits standard second-order phase transitions for most parameter ranges, with no evidence of tricritical behavior. However, for certain positive values of the anisotropies, the model displays a first-order phase transition within the ordered phase, characterized by a jump from a higher-spin ordered state to a lower-spin ordered state. The critical temperatures are shown to be sensitive to the magnitude and sign of the anisotropy parameters. In particular, negative transverse anisotropies favor magnetic order, raising the critical temperature, while positive anisotropies promote disorder, lowering the critical temperature. This study provides a comprehensive analysis of the phase diagram of the S=5/2 S = 5/2 S=5/2 quantum Blume-Capel model and highlights the role of transverse fields in modifying the critical behavior.
We investigated the critical behavior of the S=1 Blume Capel model in a scenario where the system is subject to a transverse crystalline field (D), which was randomly distributed through a bimodal probability distribution where p (1−p) corresponds to a fraction of sites that are (are not) under the action of the crystalline field. Using mean field theory based on Bogoulibov inequality for free energy, we obtain phase diagrams in the planes of the crystalline field versus temperature (D−τ) and magnetization versus temperature and (m−τ). We show that the topology of the phase diagrams depends significantly on the model parameters. The competition between temperature (τ), exchange interaction, and the random distribution of the crystalline field are responsible for revealing essential details of the critical behavior observed in the phase diagrams obtained as tricritical points (TCP) that separate the phase transition lines first and second order.
The mean-field approximation is used to calculate the phase diagrams of the spin-3/2 random transverse crystal field (RTCF) model. A bimodal distribution of the RTCF is employed in which one of the modes is in competition with the other mode whose strength is adjusted with a controllable parameter α. Thus, some sites in the lattice are under the effect of RTCF Dx with probability p and the rest of the sites are under the effect of αDx with 1 − p. The phase diagrams of the model are obtained on the RTCF-temperature planes by varying p on square lattices. Both second- and first-order phase transitions are displayed and thus tricritical points are also observed. The critical end points and end points for the first-order phase transition lines were also found.
The dynamical phase transitions of the kinetic Ising model in the presence of a random magnetic field with a bimodal probability distribution is studied by using effective-field theory (EFT) with correlations. We have used a Glauber-type stochastic dynamic to describe the time evolution of the system, where the system strongly depends on the H≡√<H(i)(2)>(c) root mean square deviation of the magnetic field. The EFT dynamic equation is given for the simple cubic lattice (z=6), and the dynamic order parameter is calculated. The system presents ferromagnetic and paramagnetic states for low and high temperatures, respectively. Our results predict first-order transitions at low temperatures and large disorder strengths, which corresponds to the existence of a nonequilibrium tricritical point (TCP) in a phase diagram in the T-H plane. We compare the results with the equilibrium phase diagram, where only the first-order line is different. Our qualitative results are compatible with recent Monte Carlo simulations.