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arXiv:cond-mat/0504483 · Physical Review B

Spin-glass behavior in the random-anisotropy Heisenberg model

Orlando V. Billoni, Sergio Alejandro Cannas, Francisco A. Tamarit

Published Sep 2, 2005• 28 citations
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Abstract

We perform Monte Carlo simulations in a random-anisotropy magnet at a intermediate exchange to anisotropy ratio. We focus on the out of equilibrium relaxation after a sudden quenching in the low temperature phase, well below the freezing one. By analyzing both the aging dynamics and the violation of the fluctuation dissipation relation we found strong evidence of a spin-glass-like behavior. In fact, our results are qualitatively similar to those experimentally obtained recently in a Heisenberg-type real spin glass.

DOI
10.1103/physrevb.72.104407

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We perform Monte Carlo simulations in a random-anisotropy magnet at a intermediate exchange to anisotropy ratio. We focus on the out of equilibrium relaxation after a sudden quenching in the low temperature phase, well below the freezing one. By analyzing both the aging dynamics and the violation of the fluctuation dissipation relation we found strong evidence of a spin-glass-like behavior. In fact, our results are qualitatively similar to those experimentally obtained recently in a Heisenberg-type real spin glass.
Spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses are studied with and without random magnetic anisotropy by dynamical Monte Carlo simulations. In the isotropic case, clear evidence of a finite-temperature chiral-glass transition is presented. While the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observed in the mean-field model. In the anisotropic case, asymptotic mixing of the spin and the chirality is observed in the off-equilibrium dynamics.
We numerically study the nonequilibrium dynamics of the three-dimensional Heisenberg Edwards-Anderson spin glass following a sudden quench to its low-temperature phase. The subsequent aging behavior of the system is analyzed in detail, and the scaling behavior of various space-time correlation functions is investigated for both spin and chiral degrees of freedom. We carefully compare our results with those obtained from simulations of the more studied Ising version of the model, and with experiments on real spin glasses in which the spins have vectorial character. Finally, the present dynamical study offers perspectives into the possibility of spin-chirality decoupling at low temperature in vectorial spin glasses.
We study the out-of-equilibrium dynamics of the infinite range quantum Heisenberg spin glass model coupled to a thermal relaxation bath. The SU(2)\mathrm{SU}(2)SU(2) spin algebra is generalized to SU(N)\mathrm{SU}(N)SU(N) and we analyze the large-NNN limit. The model displays a dynamical phase transition between a paramagnetic and a glassy phase. In the latter, the system remains out-of-equilibrium and displays an aging phenomenon, which we characterize using both analytical and numerical methods. In the aging regime, the quantum fluctuation-dissipation relation is violated and replaced over a very long time by its classical generalization, as in models involving simple spin algebras studied previously. We also discuss the effect of a finite coupling to the relaxation baths and their possible forms. This work completes and justifies previous studies on this model using a static approach.
We have studied the critical properties of the three-dimensional random anisotropy Heisenberg model by means of numerical simulations using the Parallel Tempering method. We have simulated the model with two different disorder distributions, cubic and isotropic ones, with two different anisotropy strengths for each disorder class. For the case of the anisotropic disorder, we have found evidence of universality by finding critical exponents and universal dimensionless ratios independent of the strength of the disorder. In the case of isotropic disorder distribution the situation is very involved: we have found two phase transitions in the magnetization channel which are merging for larger lattices remaining a zero magnetization low-temperature phase. Studying this region using a spin-glass order parameter we have found evidence for a spin-glass phase transition. We have estimated effective critical exponents for the spin-glass phase transition for the different values of the strength of the isotropic disorder, discussing the crossover regime.
Spin-glass (SG) and chiral-glass (CG) orderings in three-dimensional (3D) Heisenberg spin glass with and without magnetic anisotropy are studied by using large-scale off-equilibrium Monte Carlo simulations. A characteristic time of relaxation, which diverges at a transition temperature in the thermodynamic limit, is obtained as a function of the temperature and the system size. Based on the finite-size-scaling analysis for the relaxation time, it is found that in the isotropic Heisenberg spin glass, the CG phase transition occurs at a finite temperature, while the SG transition occurs at a lower temperature, which is compatible with zero. Our results of the anisotropic case support the chirality scenario for the phase transitions in the 3D Heisenberg spin glasses.