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. Implication to experimental phase diagram is discussed.Comment: 5 pages, 3 figure

Comment on ``Spin-glass transition of the three-dimensional Heisenberg spin glass''

Campos et al. [Phys. Rev. Lett. 97 (2006) 217204] claim that in the 3d Heisenberg Spin Glass, chiral and spin sector ordering temperatures are identical. We point out that in their analysis of their numerical data key assumptions are made which are unjustified.Comment: published versio

Ordering of the Heisenberg spin glass in two dimensions

The spin and the chirality orderings of the Heisenberg spin glass in two dimensions with the nearest-neighbor Gaussian coupling are investigated by equilibrium Monte Carlo simulations. Particular attention is paid to the behavior of the spin and the chirality correlation lengths. In order to observe the true asymptotic behavior, fairly large system size L\gsim 20 (L the linear dimension of the system) appears to be necessary. It is found that both the spin and the chirality order only at zero temperature. At high temperatures, the chiral correlation length stays shorter than spin correlation length, whereas at lower temperatures below the crossover temperature T_\times, the chiral correlation length exceeds the spin correlation length. The spin and the chirality correlation-length exponents are estimated above T_\times to be \nu_SG=0.9+-0.2 and \nu_CG=2.1+-0.3, respectively. These values are close to the previous estimates on the basis of the domain-wall-energy calculation. Discussion is given about the asymptotic critical behavior realized below T_\times.Comment: to appear in a special issue of J. Phys.

Creep rupture of materials: insights from a fiber bundle model with relaxation

I adapted a model recently introduced in the context of seismic phenomena, to study creep rupture of materials. It consists of linear elastic fibers that interact in an equal load sharing scheme, complemented with a local viscoelastic relaxation mechanism. The model correctly describes the three stages of the creep process, namely an initial Andrade regime of creep relaxation, an intermediate regime of rather constant creep rate, and a tertiary regime of accelerated creep towards final failure of the sample. In the tertiary regime creep rate follows the experimentally observed one over time-to-failure dependence. The time of minimum strain rate is systematically observed to be about 60-65 % of the time to failure, in accordance with experimental observations. In addition, burst size statistics of breaking events display a -3/2 power law for events close to the time of failure, and a steeper decay for the all-time distribution. Statistics of interevent times shows a tendency of the events to cluster temporarily. This behavior should be observable in acoustic emission experiments

Replica symmetry breaking transition of the weakly anisotropic Heisenberg spin glass in magnetic fields

The spin and the chirality orderings of the three-dimensional Heisenberg spin glass with the weak random anisotropy are studied under applied magnetic fields by equilibrium Monte Carlo simulations. A replica symmetry breaking transition occurs in the chiral sector accompanied by the simultaneous spin-glass order. The ordering behavior differs significantly from that of the Ising SG, despite the similarity in the global symmetry. Our observation is consistent with the spin-chirality decoupling-recoupling scenario of a spin-glass transition.Comment: 4 pages, 4 figure

Low-dimensional chaos induced by frustration in a non-monotonic system

We report a novel mechanism for the occurrence of chaos at the macroscopic level induced by the frustration of interaction, namely frustration-induced chaos, in a non-monotonic sequential associative memory model. We succeed in deriving exact macroscopic dynamical equations from the microscopic dynamics in the case of the thermodynamic limit and prove that two order parameters dominate this large-degree-of-freedom system. Two-parameter bifurcation diagrams are obtained from the order-parameter equations. Then we analytically show that the chaos is low-dimensional at the macroscopic level when the system has some degree of frustration, but that the chaos definitely does not occur without the frustration.Comment: 2 figure

Chiral exponents in O(N) x O(m) spin models at O(1/N^2)

The critical exponents corresponding to chirality are computed at O(1/N^2) in d-dimensions at the stable chiral fixed point of a scalar field theory with an O(N) x O(m) symmetry. Pade-Borel estimates for the exponents are given in three dimensions for the Landau-Ginzburg-Wilson model at m = 2.Comment: 8 latex page

On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering

The contribution of quarks with masses m >> Lambda_QCD is the only part of the structure functions in deep-inelastic scattering (DIS) which is not yet known at the next-to-next-to-leading order (NNLO) of perturbative QCD. We present improved partial NNLO results for the most important structure function F_2(x,Q^2) near the partonic threshold, in the high-energy (small-x) limit and at high scales Q^2 >> m^2; and employ these results to construct approximations for the gluon and quark coefficient functions which cover the full kinematic plane. The approximation uncertainties are carefully investigated, and found to be large only at very small values, x smaller about 10^-3, of the Bjorken variable.Comment: 62 pages, LaTeX, 13 figures. Erratum for eq.(B.7