Randomness-Induced Quantum Spin Liquid Behavior in the s=1/2 Random-Bond Heisenberg Antiferromagnet on the Pyrochlore Lattice.

We investigate the zero- and finite-temperature properties of the random-bond s=1/2 Heisenberg antiferromagnet on the pyrochlore lattice by the exact diagonalization and the Hams-de Raedt methods. We find that the randomness induces the gapless quantum spin liquid (QSL) state, the random-singlet state. Implications to recent experiments on the mixed-anion pyrochlore-lattice antiferromagnet Lu_{2}Mo_{2}O_{5}N_{2} exhibiting gapless QSL behaviors are discussed.

Ripple State in the Frustrated Honeycomb-Lattice Antiferromagnet.

We discover a new type of multiple-q state, a "ripple state," in a frustrated honeycomb-lattice Heisenberg antiferromagnet under magnetic fields. The ground state has an infinite ringlike degeneracy in the wave vector space, exhibiting a cooperative paramagnetic state, a "ring-liquid" state. We elucidate that the system exhibits the ripple state as a new low-temperature thermodynamic phase via a second-order phase transition from the ring-liquid state, keeping the ringlike spin structure factor. The spin texture in real space looks like a "water ripple" and can induce a giant electric polarization vortex. A possible relationship to the honeycomb-lattice compound, Bi_{3}Mn_{4}O_{12}(NO_{3}), is discussed.

Nature of the randomness-induced quantum spin liquids in two dimensions.

The nature of the randomness-induced quantum spin liquid state, the random-singlet state, is investigated in two dimensions (2D) by means of the exact-diagonalization and the Hams-de Raedt methods for several frustrated lattices, e.g. the triangular, the kagome and the J 1-J 2 square lattices. Properties of the ground state, the low-energy excitations and the finite-temperature thermodynamic quantities are investigated. The ground state and the low-lying excited states consist of nearly isolated singlet-dimers, clusters of resonating singlet-dimers, and orphan spins. Low-energy excitations are either singlet-to-triplet excitations, diffusion of orphan spins accompanied by the recombination of nearby singlet-dimers, creation or destruction of resonating singlet-dimers clusters. The latter two excitations give enhanced dynamical 'liquid-like' features to the 2D random-singlet state. Comparison is made with the random-singlet state in a 1D chain without frustration, the similarity and the difference between in 1D and in 2D being highlighted. Frustration in a wide sense, not only the geometrical one but also including the one arising from the competition between distinct types of interactions, play an essential role in stabilizing this frustrated random singlet state. Recent experimental situations on both organic and inorganic materials are reviewed and discussed.

Nature of the high-speed rupture of the two-dimensional Burridge-Knopoff model of earthquakes.

The nature of the high-speed rupture or the main shock of the Burridge-Knopoff spring-block model in two dimensions obeying the rate- and state-dependent friction law is studied by means of extensive computer simulations. It is found that the rupture propagation in larger events is highly anisotropic and irregular in shape on longer length scales, although the model is completely uniform and the emergent rupture-propagation velocity is nearly constant everywhere at the rupture front. The manner of the rupture propagation sometimes mimics the successive ruptures of neighbouring 'asperities' observed in real, large earthquakes. Large events tend to be unilateral, with its epicentre lying at the rim of its rupture zone. The epicentre site of a large event is also located next to the rim of the rupture zone of some past event. Event-size distributions are computed and discussed in comparison with those of the corresponding one-dimensional model. The magnitude distribution exhibits a power-law behaviour resembling the Gutenberg-Richter law for smaller magnitudes, which changes over to a more characteristic behaviour for larger magnitudes. For very large events, the rupture-length distribution exhibits mutually different behaviours in one dimension and in two dimensions, reflecting the difference in the underlying geometry.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Statistical properties of the one-dimensional Burridge-Knopoff model of earthquakes obeying the rate- and state-dependent friction law.

Statistical properties of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes obeying the rate- and state-dependent friction law are studied by extensive computer simulations. The quantities computed include the magnitude distribution, the rupture-length distribution, the main shock recurrence-time distribution, the seismic-time correlations before and after the main shock, the mean slip amount, and the mean stress drop at the main shock, etc. Events of the model can be classified into two distinct categories. One tends to be unilateral with its epicenter located at the rim of the rupture zone of the preceding event, while the other tends to be bilateral with enhanced "characteristic" features resembling the so-called "asperity." For both types of events, the distribution of the rupture length L_{r} exhibits an exponential behavior at larger sizes, ≈exp[-L_{r}/L_{0}] with a characteristic "seismic correlation length" L_{0}. The mean slip as well as the mean stress drop tends to be rupture-length independent for larger events. The continuum limit of the model is examined, where the model is found to exhibit pronounced characteristic features. In the continuum limit, the characteristic rupture length L_{0} is estimated to be ∼100 [km]. This means that, even in a hypothetical homogenous infinite fault, events cannot be indefinitely large in the exponential sense, the upper limit being of order ∼10^{3} kilometers. Implications to real seismicity are discussed.

Spin-Lattice-Coupled Order in Heisenberg Antiferromagnets on the Pyrochlore Lattice.

Effects of local lattice distortions on the spin ordering are investigated for the antiferromagnetic classical Heisenberg model on the pyrochlore lattice. It is found by Monte Carlo simulations that the spin-lattice coupling (SLC) originating from site phonons induces a first-order transition into two different types of collinear magnetic ordered states. The state realized at the stronger SLC is cubic symmetric characterized by the magnetic (1/2,1/2,1/2) Bragg peaks, while that at the weaker SLC is tetragonal symmetric characterized by the (1,1,0) ones, each accompanied by the commensurate local lattice distortions. Experimental implications to chromium spinels are discussed.

Finite-temperature transition of the antiferromagnetic Heisenberg model on a distorted kagome lattice.

Motivated by the recent experiment on kagome-lattice antiferromagnets, we study the zero-field ordering behavior of the antiferromagnetic classical Heisenberg model on a uniaxially distorted kagome lattice by Monte Carlo simulations. A first-order transition, which has no counterpart in the corresponding undistorted model, takes place at a very low temperature. The origin of the transition is ascribed to a cooperative proliferation of topological excitations inherent to the model.

Multiple-q states and the Skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields.

Ordering of the frustrated classical Heisenberg model on the triangular lattice with an incommensurate spiral structure is studied under magnetic fields by means of a mean-field analysis and a Monte Carlo simulation. Several types of multiple-q states including the Skyrmion-lattice state is observed in addition to the standard single-q state. In contrast to the Dzyaloshinskii-Moriya interaction driven system, the present model allows both Skyrmions and anti-Skyrmions, together with a new thermodynamic phase where Skyrmion and anti-Skyrmion lattices form a domain state.

The ordering of XY spin glasses.

Ordering properties of XY-like spin-glass magnets with an easy-plane magnetic anisotropy are studied based on a symmetry consideration and the results of recent numerical simulations on the pure Heisenberg and XY spin-glass models. The effects of an easy-plane-type uniaxial anisotropy, a random magnetic anisotropy and an applied magnetic field are investigated. In the XY regime in zero field, the 'spin-chirality decoupling' persists even under the random magnetic anisotropy, escaping the 'spin-chirality recoupling' phenomenon which inevitably occurs in the Heisenberg regime. Contrast between the scalar chiral order and the vector chiral order is emphasized. Implications for experiments are discussed.

Spin-chirality decoupling in the one-dimensional Heisenberg spin glass with long-range power-law interactions.

We study the issue of the spin-chirality decoupling or coupling in the ordering of the Heisenberg spin glass by performing large-scale Monte Carlo simulations on a one-dimensional Heisenberg spin-glass model with a long-range power-law interaction up to large system sizes. We find that the spin-chirality decoupling occurs for an intermediate range of the power-law exponent. Implications to the corresponding d-dimensional short-range model are discussed.

Asperity characteristics of the Olami-Feder-Christensen model of earthquakes.

Properties of the Olami-Feder-Christensen (OFC) model of earthquakes are studied by numerical simulations. The previous study indicated that the model exhibited "asperity"-like phenomena, i.e., the same region ruptures many times near periodically [T. Kotani, Phys. Rev. E 77, 010102(R) (2008)]. Such periodic or characteristic features apparently coexist with power-law-like critical features, e.g., the Gutenberg-Richter law observed in the size distribution. In order to clarify the origin and the nature of the asperity-like phenomena, we investigate here the properties of the OFC model with emphasis on its stress distribution. It is found that the asperity formation is accompanied by self-organization of the highly concentrated stress state. Such stress organization naturally provides the mechanism underlying our observation that a series of asperity events repeat with a common epicenter site and with a common period solely determined by the transmission parameter of the model. Asperity events tend to cluster both in time and in space.

Numerical evidence of spin-chirality decoupling in the three-dimensional heisenberg spin glass model.

Ordering of the three-dimensional Heisenberg spin glass with Gaussian coupling is studied by extensive Monte Carlo simulations. The model undergoes successive chiral-glass and spin-glass transitions at nonzero temperatures T_{CG}>T_{SG}>0, exhibiting spin-chirality decoupling.

Simulation study of earthquakes based on the two-dimensional Burridge-Knopoff model with long-range interactions.

Spatiotemporal correlations of the two-dimensional (2D) spring-block (Burridge-Knopoff) models of earthquakes with the long-range interblock interactions are extensively studied by means of numerical computer simulations. The long-range interaction derived from an elastic theory, which takes account of the effect of the elastic body adjacent to the fault plane, falls off with distance r as 1r;{3} . Comparison is made with the properties of the corresponding short-range models studied earlier. Seismic spatiotemporal correlations of the long-range models generally tend to be weaker than those of the short-range models. The magnitude distribution exhibits a "near-critical" behavior, i.e., a power-law-like behavior close to the Gutenberg-Richter law, for a wide parameter range with its B -value, B approximately 0.55 , insensitive to the model parameters, in sharp contrast to that of the 2D short-range model and those of the 1D short-range and long-range models where such a near-critical behavior is realized only by fine tuning the model parameters. In contrast to the short-range case, the mean stress drop at a seismic event of the long-range model is nearly independent of its magnitude, consistent with the observation. Large events often accompany foreshocks together with a doughnutlike quiescence as their precursors, while they hardly accompany aftershocks with almost negligible seismic correlations observed after the main shock.

Periodicity and criticality in the Olami-Feder-Christensen model of earthquakes.

Characteristic versus critical features of earthquakes are studied on the basis of the Olami-Feder-Christensen model. It is found that the local recurrence-time distribution exhibits a sharp delta -function-like peak corresponding to rhythmic recurrence of events with a fixed "period" uniquely determined by the transmission parameter of the model, together with a power-law-like tail corresponding to scale-free recurrence of events. The model exhibits phenomena closely resembling the asperity known in seismology.

Simulation study of spatiotemporal correlations of earthquakes as a stick-slip frictional instability.

Spatiotemporal correlations of earthquakes are studied numerically on the basis of the one-dimensional spring-block (Burridge-Knopoff) model. As large events approach, the frequency of smaller events gradually increases, while, just before the mainshock, it is dramatically suppressed in a close vicinity of the epicenter of the upcoming mainshock, a phenomenon closely resembling the "Mogi doughnut."

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 spin glass, despite the similarity in the global symmetry. Our observation is consistent with the spin-chirality decoupling-recoupling scenario of a spin-glass transition.

The role of iodine-123-labeled 15-(p-iodophenyl)-3R,S-methylpentadecanoic acid scintigraphy in the detection of local myocardial involvement of sarcoidosis.

PURPOSE: The purpose of this study is to examine the role of Iodine-123-labeled 15-(p-iodophenyl)-3R,S-methylpentadecanoic acid (BMIPP) scintigraphy in patients with cardiac sarcoidosis. METHODS AND MATERIALS: Study materials were six patients with pathologically proven cardiac sarcoidosis. BMIPP and resting Thallium-201 (201Tl) myocardial scintigraphy, echocardiography, were performed within 22 days in each patient. RESULTS: Myocardium was divided into nine areas per one case. A total of 24 areas had involvement by sarcoidosis. A total of 18 areas with defects of BMIPP accumulation and 14 areas with defects of 201Tl accumulation were detected. A total of 12 areas were determined as showing reduced wall motion. The sensitivity, specificity, positive and negative predictive values of wall motion abnormality for the detection of myocardial involvement were 50%, 100%, 100% and 71%. The sensitivities of BMIPP and 201Tl scintigraphy for the detection of local myocardial involvement were 75% and 58%. The specificities of BMIPP and 201Tl scintigraphy were both 100%. The positive predictive values of BMIPP and 201Tl scintigraphy were both 100%. The negative predictive values of BMIPP and 201Tl scintigraphy were 83% and 75%. CONCLUSION: BMIPP scintigraphy was more sensitive and had a higher negative predictive value compared to 201Tl scintigraphy and echocardiography for the detection of myocardial involvement of sarcoidosis.

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.

Anomalous Hall effect as a probe of the chiral order in spin glasses.

The anomalous Hall effect arising from the noncoplanar spin configuration (chirality) is discussed as a probe of the chiral order in spin glasses. It is shown that the Hall coefficient yields direct information about the linear and nonlinear chiral susceptibilities of the spin sector, which has been hard to obtain experimentally from the standard magnetic measurements. Based on the chirality scenario of spin-glass transition, predictions are given on the behavior of the Hall resistivity of canonical spin glasses.

Chiral Kosterlitz-Thouless transition in the frustrated Heisenberg antiferromagnet on a pyrochlore slab.

Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. In contrast to the kagomé Heisenberg antiferromagnet, the model exhibits locally noncoplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. Under certain conditions, the model exhibits a novel Kosterlitz-Thouless-type transition at a finite temperature associated with these chiral degrees of freedom.