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

Accurate random-phase approximation calculation of low-lying states on a three-dimensional Cartesian mesh

We present a simple and efficient method for calculating excitation energies and transition probabilities of low-lying states described by Hartree-Fock (HF) plus random-phase approximation (RPA) with Skyrme force. The method employs conjugate gradient method to solve the RPA equations in the mixed representation of coordinate and occupied orbitals, which was proposed recently. To obtain accurate results with coarse mesh (1 fm) calculation, we find a useful prescription. Performing self-consistently three-dimensional Cartesian mesh calculation with Lagrange mesh method in solving HF and RPA equations, we take an average of quantities calculated with even and odd mesh points in one direction. As a demonstration of our method, we show the numerical results of energies for spurious mode of translation of 16O and the excitation energies and reduced transition probabilities for first 3- state of 16O and 208Pb

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