Loop algorithm for classical Heisenberg models with spin-ice type degeneracy

In many frustrated Ising models, a single-spin flip dynamics is frozen out at low temperatures compared to the dominant interaction energy scale because of the discrete "multiple valley" structure of degenerate ground-state manifold. This makes it difficult to study low-temperature physics of these frustrated systems by using Monte Carlo simulation with the standard single-spin flip algorithm. A typical example is the so-called spin ice model, frustrated ferromagnets on the pyrochlore lattice. The difficulty can be avoided by a global-flip algorithm, the loop algorithm, that enables to sample over the entire discrete manifold and to investigate low-temperature properties. We extend the loop algorithm to Heisenberg spin systems with strong easy-axis anisotropy in which the ground-state manifold is continuous but still retains the spin-ice type degeneracy. We examine different ways of loop flips and compare their efficiency. The extended loop algorithm is applied to the following two models, a Heisenberg antiferromagnet with easy-axis anisotropy along the z axis, and a Heisenberg spin ice model with the local easy-axis anisotropy. For both models, we demonstrate high efficiency of our loop algorithm by revealing the low-temperature properties which were hard to access by the standard single-spin flip algorithm. For the former model, we examine the possibility of order-from-disorder and critically check its absence. For the latter model, we elucidate a gas-liquid-solid transition, namely, crossover or phase transition among paramagnet, spin-ice liquid, and ferromagnetically-ordered ice-rule state.Comment: 12 pages, 11 figures, accepted for publication in Phys. Rev.

Localized Distributions of Quasi Two-Dimensional Electronic States near Defects Artificially Created at Graphite Surfaces in Magnetic Fields

We measured the local density of states of a quasi two-dimensional electron system (2DES) near defects, artificially created by Ar-ion sputtering, on surfaces of highly oriented pyrolytic graphite (HOPG) with scanning tunneling spectroscopy (STS) in high magnetic fields. At valley energies of the Landau level spectrum, we found two typical localized distributions of the 2DES depending on the defects. These are new types of distributions which are not observed in the previous STS work at the HOPG surface near a point defect [Y. Niimi \textit{et al}., Phys. Rev. Lett. {\bf 97}, 236804 (2006).]. With increasing energy, we observed gradual transformation from the localized distributions to the extended ones as expected for the integer quantum Hall state. We show that the defect potential depth is responsible for the two localized distributions from comparison with theoretical calculations.Comment: 4 pages, 3 figure

Spin-glass transition in bond-disordered Heisenberg antiferromagnets coupled with local lattice distortions on a pyrochlore lattice

Motivated by puzzling characteristics of spin-glass transitions widely observed in pyrochlore-based frustrated materials, we investigate effects of coupling to local lattice distortions in a bond-disordered antiferromagnet on the pyrochlore lattice by extensive Monte Carlo simulations. We show that the spin-glass transition temperature \TSG is largely enhanced by the spin-lattice coupling, and furthermore, becomes almost independent of $\Delta$ in a wide range of the disorder strength $\Delta$. The critical property of the spin glass transition is indistinguishable from that of the canonical Heisenberg spin glass in the entire range of $\Delta$. These peculiar behaviors are ascribed to a modification of the degenerate manifold from continuous to semidiscrete one by the spin-lattice coupling.Comment: 4 pages, 3 figures, major revisions, accepted for publication in PR