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.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.

arXiv:cond-mat/0204225Physical review. B, Condensed matterSep 4, 200222 citations

Relaxation in spin glasses

I. Riess, Moshe Fibich, A. Ron

Journal of Magnetism and Magnetic MaterialsJan 1, 19781 citation

Dynamic scaling and the field-dependent critical line in a fractal cluster model of spin glasses

M. A. Contínentino, A. P. Malozemoff

We extend an earlier fractal cluster model of spin glasses to study (1) the magnetization relaxation M(t) induced by a magnetic field, (2) magnetic noise, and (3) dynamics near a critical line ${T}_{g}$ (H). Above the zero-field transition temperature ${T}_{g}$ , M(t) follows a stretched exponential form exp(-${t}^{1\mathrm{\ensuremath{-}}n}$) with n=\ensuremath{\nu}z/(\ensuremath{\varphi}+\ensuremath{\nu}z), where \ensuremath{\varphi},\ensuremath{\nu}, and z are standard static and dynamical critical exponents. A dynamic scaling relation is derived for the entire region ${T}_{g}$ (H) ${T}_{g}$ in agreement with experiments. The equations associated with lines of constant relaxation time are obtained and it is shown how nonuniversality of exponents along the critical line can be tested.We extend an earlier fractal cluster model of spin glasses to study (1) the magnetization relaxation M(t) induced by a magnetic field, (2) magnetic noise, and (3) dynamics near a critical line ${T}_{g}$(H). Above the zero-field transition temperature ${T}_{g}$, M(t) follows a stretched exponential form exp(-${t}^{1\mathrm{\ensuremath{-}}n}$) with n=\ensuremath{\nu}z/(\ensuremath{\varphi}+\ensuremath{\nu}z), where \ensuremath{\varphi},\ensuremath{\nu}, and z are standard static and dynamical critical exponents. A dynamic scaling relation is derived for the entire region ${T}_{g}$(H)${T}_{g}$ in agreement with experiments. The equations associated with lines of constant relaxation time are obtained and it is shown how nonuniversality of exponents along the critical line can be tested.

Physical review. B, Condensed matterMar 1, 198644 citations

Dynamical ac study of the critical behavior in Heisenberg spin glasses

Marco Picco, Félix Ritort

We present some numerical results for the Heisenberg spin-glass model with Gaussian interactions, in a three-dimensional cubic lattice. We measure the ac susceptibility as a function of temperature and determine an apparent finite temperature transition which is compatible with the chiral-glass temperature transition for this model. The relaxation time diverges like a power law $\ensuremath{\tau}\ensuremath{\sim}{(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}z\ensuremath{\nu}}$ with ${T}_{c}=0.19(4)$ and $z\ensuremath{\nu}=5.0(5)$. Although our data indicate that the spin-glass transition occurs at the same temperature as the chiral glass transition, we cannot exclude the possibility of a chiral-spin coupling scenario for the lowest frequencies investigated.We present some numerical results for the Heisenberg spin-glass model with Gaussian interactions, in a three-dimensional cubic lattice. We measure the ac susceptibility as a function of temperature and determine an apparent finite temperature transition which is compatible with the chiral-glass temperature transition for this model. The relaxation time diverges like a power law $\ensuremath{\tau}\ensuremath{\sim}{(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}z\ensuremath{\nu}}$ with ${T}_{c}=0.19(4)$ and $z\ensuremath{\nu}=5.0(5)$. Although our data indicate that the spin-glass transition occurs at the same temperature as the chiral glass transition, we cannot exclude the possibility of a chiral-spin coupling scenario for the lowest frequencies investigated.

arXiv:cond-mat/0405308Physical Review BMar 18, 200527 citations

Relaxation in quantum spin glasses

Bosiljka Tadić, R. Pirc, R. Blinc +1 more

Journal of Non-Crystalline SolidsSep 1, 19940 citations

We extend an earlier fractal cluster model of spin glasses to study (1) the magnetization relaxation M(t) induced by a magnetic field, (2) magnetic noise, and (3) dynamics near a critical line

{T}_{g}

(H). Above the zero-field transition temperature

{T}_{g}

, M(t) follows a stretched exponential form exp(-${t}^{1\mathrm{\ensuremath{-}}n}$) with n=\ensuremath{\nu}z/(\ensuremath{\varphi}+\ensuremath{\nu}z), where \ensuremath{\varphi},\ensuremath{\nu}, and z are standard static and dynamical critical exponents. A dynamic scaling relation is derived for the entire region

{T}_{g}

(H)

{T}_{g}

in agreement with experiments. The equations associated with lines of constant relaxation time are obtained and it is shown how nonuniversality of exponents along the critical line can be tested.

{T}_{c}=0.19(4)

and $z\ensuremath{\nu}=5.0(5)$. Although our data indicate that the spin-glass transition occurs at the same temperature as the chiral glass transition, we cannot exclude the possibility of a chiral-spin coupling scenario for the lowest frequencies investigated.