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Journal of Petrochemical Universities

The Ground-State Magnetic Properties of the Single-Ion Anisotropy Ising Model in Transverse Field

Jie Zhao, XU Xing-guang, Guozhu Wei

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The spin-2 Ising model with singleion anisotropies was studied in the transverse magnetic field.Using the mean-field theory,based on Bogoliubov inequality and used the Gibbs free energy as standard,the theoretic expressions of ground-state magnetic moment and free energy of system were deduced.The influences of single-ion anisotropy D and transverse field Ω on the magnetization and free energy curves of spin system at ground state were mainly explored and the characteristic of first order and second order phase transition was observed from magnetization curves.It is found that there are three kinds of magnetization curves with the change of single-ion anisotropy and the trans-verse magnetic field: first,the magnetic moment of the Ising system suddenly decreases from 2 to 1,which exhibits first order-order phase transition;second,the magnetic moment suddenly changes from 2 or 1 to 0,which exhibits first order-disorder phase transition;third,the magnetic moment smoothly changes from 2 or 1 to 0,which exhibits second order-disorder phase transition.The results show that first order-order (2-1),first order-disorder(1-0) phase transitions disappear one after another with the increasing of transverse field Ω in the m-D/(zJ) ground state magnetization curves.At the same time first order-order(2-1),first order-disorder(1-0) phase transitions also disappear in the same way with the increase of the single-ion anisotropy D in the m-D/(zJ) ground state magnetization curves.It is also found that the free energy always decreases when Ω or D increases through analysis of free energy curves at ground state.

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Communications in Theoretical Physics•Jun 1, 2006•5 citations
The spin-2 Ising model with singleion anisotropies was studied in the transverse magnetic field.Using the mean-field theory,based on Bogoliubov inequality and used the Gibbs free energy as standard,the theoretic expressions of ground-state magnetic moment and free energy of system were deduced.The influences of single-ion anisotropy D and transverse field Ω on the magnetization and free energy curves of spin system at ground state were mainly explored and the characteristic of first order and second order phase transition was observed from magnetization curves.It is found that there are three kinds of magnetization curves with the change of single-ion anisotropy and the trans-verse magnetic field: first,the magnetic moment of the Ising system suddenly decreases from 2 to 1,which exhibits first order-order phase transition;second,the magnetic moment suddenly changes from 2 or 1 to 0,which exhibits first order-disorder phase transition;third,the magnetic moment smoothly changes from 2 or 1 to 0,which exhibits second order-disorder phase transition.The results show that first order-order (2-1),first order-disorder(1-0) phase transitions disappear one after another with the increasing of transverse field Ω in the m-D/(zJ) ground state magnetization curves.At the same time first order-order(2-1),first order-disorder(1-0) phase transitions also disappear in the same way with the increase of the single-ion anisotropy D in the m-D/(zJ) ground state magnetization curves.It is also found that the free energy always decreases when Ω or D increases through analysis of free energy curves at ground state.
The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/zJ-longitudinal crystal D/zJ field plane. We find that there are the first order-order phase transitions in a very small range of D/zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions.
Using the correlated effective-field theory,the spin-2 transverse Ising model with the crystal field for the square lattice has been investigated.The expressions of magnetization were obtained and by numerical calculation the ground-state magnetization curves were given.It was found that there were the first order-order phase transitions,the first order-disorder phase transitions and the second order phase transitions in the ground state.The second order transitions are widespread,and the first order transitions are occurred in the very narrow range of crystal field and transverse field.
The transverse high-spin Ising model with different single-ion anisotropies is studied in the ground state within the mean-field theory and the correlated effective-field theory.The expressions of magnetization and energy in the finite temperature and ground state are derived and the results are got numerically.The ground-state phase diagram is obtained within the mean-field theory,and the ground-state phase diagrams for the honeycomb lattice,the square lattice and the simple cubic lattice are gained,respectively,within the correlated effective theory.The focus of this paper is on the difference of phase transition properties within the mean-field theory and the correlated effective-field theory.
The ground state properties of the two-sublattice Ising metamagnet in the transverse field are studied introducing the mean-field theory. A phase diagram is given via the h-Ω rectanguler coordinates where h is the longitudinal field and Ω is the transverse field. The ground state energy, the longitudinal total magnetization, staggered magnetization and susceptibility and the transverse total magnetization are all calculated. The results show that when the transverse field Ω is small but the longitudinal field h great, the first-order transition occurs, and when the former is great but the later small the second-order transition occurs in the system. The effect of the transverse field Ω on the ground state properties of the two-sublattice Ising metamagnet is important.
We study the thermodynamic properties of random transverse field mixed spin system in the presence of single-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, the detailed phase diagrams are described and some interesting results are found under trimodal random transverse field distribution. A small single-ion anisotropy can magnify magnetic ordering region at low temperatures and existence of a large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phase transitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodal transverse field distribution.
Within the framework of an effective field approximation, the effects of single-ion anisotropy and different trimodal transverse fields of two sublattices on the critical properties of the mixed spin-1/2 and spin-1 Ising system are investigated on the simple cubic lattice. A smaller single-ion anisotropy can magnify magnetic ordering phases and a larger one can depress magnetic ordering phase for T -Ω 1/2 space at low temperatures, while a smaller single-ion anisotropy can hardly change the value of critical transverse field for T -Ω 1 space. On the other hand, influences of two different trimodal transverse fields concentrations on tricritical points and magnetic ordering phases take on some interesting results in T - D space. The main reason comes from the common action of single-ion anisotropy, different transverse fields and two trimodal distributions.