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Chinese Physics Letters

Translational Invariance in Phase Diagram of S = 1／2, 3／2 Spin Glass Systems

商育民, K.L. Yao

Published Jan 1, 2005• 0 citations
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Abstract

By using the replica method and the functional integral technique, the quantum XY spin glass model with ferromagnetic coupling is investigated numerically. From the numerical results of the thermodynamic and magnetic quantities we found that these quantities do not vary with the mean exchange interaction when the mean exchange interaction is lower than 1. This feature demonstrates that there are the mean interaction translational symmetries in the spin-glass and paramagnetic phases.

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By using the replica method and the functional integral technique, the quantum XY spin glass model with ferromagnetic coupling is investigated numerically. From the numerical results of the thermodynamic and magnetic quantities we found that these quantities do not vary with the mean exchange interaction when the mean exchange interaction is lower than 1. This feature demonstrates that there are the mean interaction translational symmetries in the spin-glass and paramagnetic phases.
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.
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.
The phase diagram of the ppp-spin-interacting spin glass model in a transverse field is investigated in the limit p→∞p \to \inftyp→∞ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit p→∞p \to \inftyp→∞ by using the large-ppp expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.
The phase diagram of modified random-bond Ising model has been investigated. The model is based on random-bond Ising model in which the distribution of magnetic interaction is Gaussian rather than the uniform distribution. The center of the distribution is positive so that most of the interactions are ferromagnetic. However the width of the distribution can be varied. The increasing of the width (J) induces disorder to this system. It is expected that when the tail of the distribution reaches the negative interaction region, the system at low temperature shows the cross over between ferromagnetic phase and spin glass phase. By using magnetization and spin glass magnetization, three ordered phases appear in the J-T phase diagram: (1) the ferromagnetic (FM) phase; (2) the spin glass (SG) phase; (3) the paramagnetic (PM) phase. At very high temperature the system is in paramagnetic phase. At low temperature and small distribution the system is in ferromagnetic phase. The cross over between ferromagnetic phase and spin glass phase is visible as the width of the interaction distribution is increase at low temperature. The critical temperature has been obtained by using Binder cumulant of spin glass magnetization.