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Physical review. B, Condensed matter

Influence of uniaxial anisotropy on a quantumXYspin-glass model with ferromagnetic coupling

Yumin Shang, K.L. Yao

Published Aug 14, 2003• 2 citations
Publisher

Abstract

In the replica symmetric approximation and the static limit in Matsubara ``imaginary time,'' we have investigated a quantum XY spin-glass system with the ferromagnetic coupling and the uniaxial anisotropy numerically. We found that, for $S=1,$ under the uniaxial anisotropy, the spin-glass phase breaks into two phases: a longitudinal spin-glass phase, and a spin-glass phase; the mixed phase of the spin glass and the ferromagnet breaks into two phases: a mixed phase of the longitudinal spin glass and the longitudinal ferromagnet, a mixed phase of the spin glass and the ferromagnet; the peak in the curve of the specific heat versus temperature is split into two peaks: the peak of uniaxial anisotropy and the peak of the ferromagnetic coupling. The system will be dominated by the random exchange interaction if the probability of the random exchange interaction taking negative value is greater than 15.87%. In the absence of the uniaxial anisotropy, there is a mean-interaction translational invariance in the spin-glass phase and the paramagnetic phase. In the presence of the uniaxial anisotropy, there is a mean-interaction translational invariance in the spin-glass phase, the longitudinal spin-glass phase and the paramagnetic phase. In these phases, the entropy, the specific heat and the susceptibility do not depend on the mean-interaction.

DOI
10.1103/physrevb.68.054410

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In the replica symmetric approximation and the static limit in Matsubara ``imaginary time,'' we have investigated a quantum XY spin-glass system with the ferromagnetic coupling and the uniaxial anisotropy numerically. We found that, for S=1,S=1,S=1, under the uniaxial anisotropy, the spin-glass phase breaks into two phases: a longitudinal spin-glass phase, and a spin-glass phase; the mixed phase of the spin glass and the ferromagnet breaks into two phases: a mixed phase of the longitudinal spin glass and the longitudinal ferromagnet, a mixed phase of the spin glass and the ferromagnet; the peak in the curve of the specific heat versus temperature is split into two peaks: the peak of uniaxial anisotropy and the peak of the ferromagnetic coupling. The system will be dominated by the random exchange interaction if the probability of the random exchange interaction taking negative value is greater than 15.87%. In the absence of the uniaxial anisotropy, there is a mean-interaction translational invariance in the spin-glass phase and the paramagnetic phase. In the presence of the uniaxial anisotropy, there is a mean-interaction translational invariance in the spin-glass phase, the longitudinal spin-glass phase and the paramagnetic phase. In these phases, the entropy, the specific heat and the susceptibility do not depend on the mean-interaction.
The quantum XY spin glass model with longitudinal ferromagnetic coupling is investigated in static replica symmetry limit. Several thermodynamic quantities are calculated numerically. We find that the ferromagnetic coupling enhances the stability of replica symmetric solution. A 2-dimensional Ising model like transition is found, which demonstrates that the ferromagnetic coupling increases the order of spin glass model. Affected by the ferromagnetic coupling, transverse component of the susceptibility has two cusps corresponding to transverse-longitudinal spin-glass phase transition and longitudinal spin glass-paramagnetic transition separately.
We study the anisotropic Heisenberg spin-glass model in a three-dimensional hierarchical lattice (designed to approximate the cubic lattice), within a real-space renormalization-group approach. Two different initial probability distributions for the exchange interaction (JijJ_{ij}Jij​), Gaussian and uniform, are used, with zero mean and width Jˉ\bar{J}Jˉ. The (kT/Jˉ)×Δ0(kT/\bar{J}) \times \Delta_0(kT/Jˉ)×Δ0​ phase diagram is obtained, where TTT is the temperature, Δ0\Delta_0Δ0​ is the first moment of the probability distribution for the uniaxial anisotropy, and kkk is the Boltzmann constant. For the Ising model (Δ0=1\Delta_0=1Δ0​=1), there is a spin-glass phase at low temperatures (high Jˉ\bar{J}Jˉ) and a paramagnetic phase at high temperatures (low Jˉ\bar{J}Jˉ). For the isotropic Heisenberg model (Δ0=0\Delta_0=0Δ0​=0), our results indicate no spin-glass phase at finite temperatures. The transition temperature between the spin-glass and paramagnetic phase decreases with Δ0\Delta_0Δ0​, as expected, but goes to zero at a finite value of the anisotropy parameter, namely Δ0=Δc∼0.59\Delta_0 = \Delta_c \sim 0.59Δ0​=Δc​∼0.59. Our results indicate that the whole transition line, between the paramagnetic and the spin-glass phases, for Δc≤Δ0<1\Delta_c \leq \Delta_0 < 1Δc​≤Δ0​<1, belongs to the same universality class as the transition for the Ising spin glass.
In the generalized quantum replica symmetric approximation, a quantum XY spin-glass model with ferromagnetic coupling and planar Dzyaloshinski–Mariya (DM) interactions is investigated theoretically. Entropy and specific heat are calculated numerically as well as spin self-interactions and spin-glass order parameters for spin . It is found that the double-cusp of the specific heat, which corresponds to the collinear ferromagnetic and the paramagnetic ferromagnetic transitions respectively, coincides completely due to DM-anisotropy interactions. Additionally, the local susceptibility and the spontaneous magnetization are evaluated numerically.
In the static replica symmetric approximation, a quantum Heisenberg S=1 spin-glass model with single-ion uniaxial anisotropy and infinite-range random Dzyaloshinskii-Moriya (DM) interaction in applied magnetic fields is investigated. The local susceptibility and the corresponding order parameters are calculated numerically, and are found to be in good agreement with those of thermofield dynamics. The dependences of entropy and specific heat on temperature are studied numerically at various magnetic fields. It is shown that the entropy is always positive and the quantum fluctuation has a very strong effect on the specific heat. Especially, the typical crossover behaviour of the specific heat of a spin glass at various magnetic fields for mixed-anisotropy interactions is found.