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Journal of Northeastern University

Ground State Properties of Ising Metamagnet in Transverse Field

Qi Zhang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

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.

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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.
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 critical properties of the one-dimensional spin-1/2 transverse Ising model in the presence of a longitudinal magnetic field were studied by the quantum fidelity method. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the fidelity susceptibility was used to locate the various phase boundaries present in the system. The type of dominant spin ordering for each phase was identified by examining the corresponding ground-state eigenvector. For a given antiferromagnetic nearest-neighbor interaction J_{2}, we calculated the fidelity susceptibility as a function of the transverse field B_{x} and the longitudinal field B_{z}. The phase diagram in the (B_{x},B_{z})-plane shows three phases. These findings are in contrast with the published literature that claims that the system has only two phases. For B_{x}<1, we observed an antiferromagnetic phase for small values of B_{z} and a paramagnetic phase for large values of B_{z}. For B_{x}>1 and low B_{z}, we found a disordered phase that undergoes a second-order phase transition to a paramagnetic phase for large values of B_{z}.
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 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.