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

Phase transition of the three-dimensional chiral Ginzburg-Landau model -- search for the chiral phase

Nature of the phase transition of regularly frustrated vector spin systems in three dimensions is investigated based on a Ginzburg-Landau-type effective Hamiltonian. On the basis of the variational analysis of this model, Onoda et al recently suggested the possible occurrence of a chiral phase, where the vector chirality exhibits a long-range order without the long-range order of the spin [Phys. Rev. Lett. 99, 027206 (2007)]. In the present paper, we elaborate their analysis by considering the possibility of a first-order transition which was not taken into account in their analysis. We find that the first-order transition indeed occurs within the variational approximation, which significantly reduces the stability range of the chiral phase, while the chiral phase still persists in a restricted parameter range. Then, we perform an extensive Monte Carlo simulation focusing on such a parameter range. Contrary to the variational result, however, we do not find any evidence of the chiral phase. The range of the chiral phase, if any, is estimated to be less than 0.1% in the temperature width.Comment: 19 pages, 17 figure

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 randaom magnetic anisotropy by dynamical Monte Carlo simulations. In 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 reminisecnt of the one observed in the mean-field model. In anisotropic case, asymptotic mixing of the spin and the chirality is observed in the off-equilibrium dynamics.Comment: 4 pages including 5 figures, LaTex, to appear in Phys. Rev. Let

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.

Electroweak Sudakov at two loop level

We investigate the Sudakov double logarithmic corrections to the form factor of fermion in the SU(2)XU(1) electroweak theory. We adopt the familiar Feynman gauge and present explicit calculations at the two loop level. We show that the leading logarithmic corrections coming from the infrared singularities are consistent with the "postulated" exponentiated electroweak Sudakov form factor. The similarities and differences in the "soft" physics between the electroweak theory and the unbroken non-abelian gauge theory (QCD) will be clarified.Comment: 8 pages, 14 figure

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

Transversely Polarized Drell-Yan Process and Soft Gluon Resummation in QCD

We calculate the transverse-momentum $Q_T$ spectrum of the dilepton in the transversely polarized Drell-Yan process on the basis of the factorization theorem in QCD. We take into account universal logarithmically enhanced corrections in edge region of phase space by resumming multiple soft-gluon emissions to all orders in the small $Q_T$ region.Comment: 84 pages, 5 figures, Revised version published in Prog.Theor.Phy

Ordering of the Heisenberg Spin Glass in High Dimensions

Ordering of the Heisenberg spin glass with the nearest-neighbor Gaussian coupling is investigated by equilibrium Monte Carlo simulations in four and five dimensions. Ordering of the mean-field Heisenberg spin-glass is also studied for comparison. Particular attention is paid to the nature of the spin-glass and the chiral-glass orderings. Our numerical data suggest that, in five dimensions, the model exhibits a single spin-glass transition at a finite temperature, where the spin-glass order accompanying the simultaneous chiral-glass order sets in. In four dimensions, by contrast, the model exhibits a chiral-glass transition at a finite temperature, not accompanying the standard spin-glass order. The critical region associated with the chiral-glass transition, however, is very narrow, suggesting that dimension four is close to the marginal dimensionality.Comment: 18 pages, 12 figure