Three-dimensional Heisenberg Spin Glass Research Articles

Fluctuation–dissipation ratio of the Heisenberg spin glass

Abstract Fluctuation–dissipation relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation.

Fluctuation-dissipation ratio of the Heisenberg spin glass.

The fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. The numerically determined FD ratio exhibits a "one-step-like" behavior, the effective temperature of the spin-glass state being about twice the spin-glass transition temperature, T(eff) approximately 2T(g), irrespective of the bath temperature. The results are discussed in conjunction with the recent experiment by Hérisson and Ocio, and with the chirality scenario of the spin-glass transition.

Dynamical critical phenomena in three-dimensional 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.

Ordering of the three-dimensional Heisenberg spin glass in magnetic fields.

Spin and chirality orderings of the three-dimensional Heisenberg spin glass are studied under magnetic fields in light of the recently developed spin-chirality decoupling-recoupling scenario. It is found by Monte Carlo simulations that the chiral-glass transition and the chiral-glass ordered state, which are essentially of the same character as their zero-field counterparts, occur under magnetic fields. The implication to the experimental phase diagram is discussed.

Monte Carlo Studies of the Ordering of the Three-Dimensional Isotropic Heisenberg Spin Glass in Magnetic Fields

Spin and chirality orderings of the three-dimensional Heisenberg spin glass under magnetic fields are studied by large-scale equilibrium Monte Carlo simulations. It is found that the chiral-glass transition and the chiral-glass ordered state, which are essentially of the same character as their zero-field counterparts, occur under magnetic fields. The chiral-glass ordered state exhibits a one-step-like peculiar replica-symmetry breaking in the chiral sector, while it does not accompany the spin-glass order perpendicular to the applied field. Critical perperties of the chiral-glass transition are different from those of the standard Ising spin glass. Magnetic phase diagram of the model is constructed, which reveals that the chiral-glass state is quite robust against magnetic fields. The chiral-glass transition line has a character of the Gabay-Toulouse line of the mean-field model, yet its physical origin being entirely different. These numerical results are discussed in light of the recently developed spin-chirality decoupling-recoupling scenario. Implication to experimental phase diagram is also discussed.

Chiral-glass transition and replica symmetry breaking of a three-dimensional heisenberg spin glass

Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a finite-temperature chiral-glass transition without the conventional spin-glass order is established. Critical exponents characterizing the transition are different from those of the standard Ising spin glass. The calculated overlap distribution suggests the appearance of a peculiar type of replica-symmetry breaking in the chiral-glass ordered state.

DYNAMICAL ASPECTS OF EQUILIBRIUM AND OFF-EQUILIBRIUM SIMULATIONS OF A THREE-DIMENSIONAL HEISENBERG SPIN GLASS

Spin-glass and chiral-glass orderings of a three-dimensional isotropic Heisenberg spin glass are studied both by equilibrium and off-equilibrium Monte Carlo simulations with emphasis on their dynamical aspects. The model is found to exhibit a finite-temperature chiral-glass transition without the conventional spin-glass order. Although chirality is an Ising-like quantity from symmetry, universality class of the chiral-glass transition appears to be different from that of the standard Ising spin glass. In the off-equilibrium simulation, while the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observered in the mean-field model.

Dynamical Simulation of Spin-Glass and Chiral-Glass Orderings in Three-Dimensional Heisenberg Spin Glasses

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.

Equilibrium simulation of chiral-glass order in a three-dimensional Heisenberg spin glass

Spin-glass and chiral-glass ordering of the three-dimensional Heisenberg spin glass with random Gaussian couplings are investigated by means of a Monte Carlo simulation based on an extended ensemble method.

Spin-glass ordering in three-dimensional Heisenberg systems.

We argue that semimagnetic semiconductors are Heisenberg systems, exhibit spin-glass ordering at finite temperature, and obey power-law scaling with universal critical exponents. A theoretical argument is presented that supports spin-glass ordering in three-dimensional Heisenberg spin glasses with short-range antiferromagnetic interactions.

Computer simulation of the three-dimensional short-range Heisenberg spin glass.

The results of large-scale Monte Carlo simulations on a nearest-neighbor Heisenberg spin-glass model are presented. We find that the transition is at zero temperature and that 3 is below the lower critical dimension. Relaxation times follow conventional dynamical scaling and diverge with a power of the temperature T as T\ensuremath{\rightarrow}0.

Nature of Ordering in Spin-Glasses

A new equilibrium characterization of the spin-glass-paramagnet transition is presented. It is based on the size dependence of the sensitivity of the free energy to the boundary conditions. Results of numerical studies of a three-dimensional Heisenberg spin-glass at $T=0$ are consistent with an algebraic decay of this sensitivity and suggest a zero-temperature phase transition.