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Materials science : an Indian journal

The critical values of ising model with the interaction of the second neighbor in the presence of DM interaction and magnetic field

H. Arefazar, Mohammad Reza Soltani

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

The Ising three qubit model has been studied by the interaction of the second neighbor in the presence of DM interaction and external longitudinal uniformmagnetic field.WeÂ’ve studied the critical values of DM interaction in the absence of magnetic field and also in the presence of magnetic field. In this case, it has been shown that the critical value of DM interaction depends on the exchange coefficient parameters and also the magnetic field. WeÂ’ve studied the critical value of the external longitudinal magnetic field per different cases of the exchange coefficients and DMinteraction power. In has been shown that in some cases, there is no critical value of magnetic field.

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The Ising three qubit model has been studied by the interaction of the second neighbor in the presence of DM interaction and external longitudinal uniformmagnetic field.WeÂ’ve studied the critical values of DM interaction in the absence of magnetic field and also in the presence of magnetic field. In this case, it has been shown that the critical value of DM interaction depends on the exchange coefficient parameters and also the magnetic field. WeÂ’ve studied the critical value of the external longitudinal magnetic field per different cases of the exchange coefficients and DMinteraction power. In has been shown that in some cases, there is no critical value of magnetic field.
In this paper, we investigate the role of Dzyaloshinski–Moriya (DM) interaction in the pairwise entanglement in the three- and four-qubit XX models with magnetic field. In the four-qubit model, the pairwise entanglements of two nearest-neighbor qubits and two next-neighbor qubits are investigated, respectively. The dependences of the critical temperature at which the pairwise thermal entanglement disappears on DM interaction and magnetic fields are studied in details. At zero temperature, the entanglement can undergo sudden changes with adjustment of the parameters, and the general results of the concurrence are obtained in all cases.
Abstract The ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field interaction in the absence and presence of a longitudinal magnetic field on a three-dimensional cubic lattice is studied within the framework both of the mean-field approximation (MFA) and Monte Carlo simulation (MCS). Using the MFA, we have shown the phase diagram of the model for zero magnetic field in the (anisotropy, temperature) plane in which the system exhibits first- and second-order phase transitions and critical end-points. Also, we have used the standard MCS to confirm the previous results; we have presented the temperature dependence of the sublattice and total magnetizations for different values of anisotropy in order to determine the phase diagram of the model in the absence of a longitudinal magnetic field. In addition, the influence of this last field on the magnetic properties of the model is investigated and discussed.
In this work, the critical properties of the classical spin-1 Ising Hamiltonian applied to magnetic systems characterized by the first-neighbors biquadratic exchange, the anisotropy and the external magnetic field contributions are theoretically investigated. The first-neighbors bilinear exchange interaction is set equal to zero. For magnetic systems the bicubic exchange interaction must be set equal to zero as it would break the time-reversal invariance of the exchange Hamiltonian. To determine the critical behavior, the spin-1 Ising Hamiltonian is mapped onto the spin-1/2 Ising Hamiltonian by using the Griffith’s variable transformation. The critical surface of a 2D square magnetic lattice is determined in the parameter space as a function of the magnetic parameters and the phase transition occurring across it is quantitatively discussed by calculating, for each spin, the free energy and the magnetization. The free energy of the 2D square magnetic lattice, described via the three-state spin-1 Ising model, is obtained from an empirical expression of the partition function recently proposed for a spin-1/2 Ising model in an external magnetic field and applied to a 2D magnetic lattice. These results could pave the way to numerical simulations and to measurements able to confirm the analytical predictions.
Three-Qubit Ground State and Thermal Entanglement of XXZXXZXXZ Model With Dzyaloshinskii-Moriya Interaction
We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubit anisotropic Heisenberg (XXZ) and Ising in a magnetic field models and in the presence of Dzyaloshinskii-Moriya (DM) interaction. We have found that increasing of the DM interaction and magnetic field can enhance and reduce the entanglement of system. We have shown that the non-symmetric pairwise has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise. For negative anisotropy the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in details. The most remarkable result happens at zero temperature where 3-qubit ground state entanglement of the system (in spite of 2-qubit counterpart) shows the fingerprint of quantum phase transition for an infinite size system.
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}.