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Science Technology and Engineering

The Ground-state Magnetic Properties of High-spin Transverse Ising Model

Jie Zhao

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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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 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.
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 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.