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中国物理B：英文版

Phase diagrams of spin-3/2 Ising model in the presence of random crystal field within the effective field theory based on two approximations

Ali, Yigit, Erhan, Albayrak

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

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.

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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.
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 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 bimodal random field quantum spin-32\frac{3}{2}23​ Ising system is investigated by combining the pair approximation with the discretized path-integral representation. The second-order phase transition lines, and tricritical points are obtained for the bimodal random field distribution. Reentrant phase transitions, which may be caused by the competition between quantum effects and randomness, are observed. The phase diagrams with respect to the random field and the second-order phase transition temperature, i.e., (H, T) plane, are studied extensively for given values of the transverse field G and the coordination number z.
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In this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic Ising system consisting of magnetic atoms with spin-1. This study is done using the effectivefield theory (EFT) with correlations method. The equations are derived using a probability distribution method based on the use of exact Van der Waerden identities. We present our numerical results, such as the phase diagrams, the thermal variations of the transverse magnetization, the internal energy, the magnetic specific heat as a function of different values of p, the concentration of the random transverse field. As a result, the critical values of transverse field , temperature and concentration were obtained for the square lattice.