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Journal de Physique Lettres

Critical relaxation in three-dimensional spin glasses

M. V. Feigel’man, L. B. Ioffe

Published Jan 1, 1985• 13 citations
Publisher

Abstract

The analytical theory of slow relaxation of the Ising and vector 3-D spin glasses with the finite range interaction near the freezing transition point Tf has been developed. In the Ising case, the maximum relaxation time tmax increases as tmax ∼ ( T - Tf)-6 exp[C(T - T f)-1/4]. For the Heisenberg spins tmax ∼ (T - T f)-10.5. It is shown that the inclusion of weak random-anisotropy exchange leads to the Ising asymptotics for t max in the Heisenberg spin glass.

DOI
10.1051/jphyslet:019850046015069500

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The analytical theory of slow relaxation of the Ising and vector 3-D spin glasses with the finite range interaction near the freezing transition point Tf has been developed. In the Ising case, the maximum relaxation time tmax increases as tmax ∼ ( T - Tf)-6 exp[C(T - T f)-1/4]. For the Heisenberg spins tmax ∼ (T - T f)-10.5. It is shown that the inclusion of weak random-anisotropy exchange leads to the Ising asymptotics for t max in the Heisenberg spin glass.
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.
A short-range \ifmmode\pm\else\textpm\fi{}J Heisenberg spin glass with and without anisotropy on a simple cubic lattice is studied by using a hybrid Monte Carlo spin-dynamics method. The anisotropy leads to a cusplike peak of the susceptibility \ensuremath{\chi} and a very slow relaxation of the spin configuration at low temperatures. From a finite-size-scaling analysis of the spin-glass susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{sg}}$, we find, for the first time, that the anisotropy induces a phase transition.
By using frustration-preserving hard-spin mean-field theory, we investigated the phase-transition dynamics in the three-dimensional field-free ± J Ising spin-glass model. As the temperature T is decreased from paramagnetic phase at high temperatures, with a rate ω=-dT/dt in time t, the critical temperature depends on the cooling rate through a clear power law ω^{a}. With increasing antiferromagnetic bond fraction p, the exponent a increases for the transition into the ferromagnetic case for p<p_{c} and decreases for the transition into the spin-glass phase for p>p_{c}, signaling the ferromagnetic - spin-glass phase transition at p_{c}≈0.22. The relaxation time is also investigated in the adiabatic case ω=0 and the dynamic exponent zν is found to increase with increasing p.
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 Tc=0.19(4){T}_{c}=0.19(4)Tc​=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.