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Hikaru Kawamura

Publications and source records attributed to Hikaru Kawamura.

At least 73 records · Page 4Linked to original sources
arXiv2009

Monte Carlo studies of the chiral and spin orderings of the three-dimensional Heisenberg spin glass

The nature of the ordering of the three-dimensional isotropic Heisenberg spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. Several independent physical quantities are measured both for the spin and for the chirality, including the correlation-length ratio, the Binder ratio, the glass order parameter, the overlap distribution function and the non-self-averageness parameter. By controlling the effect of the correction-to-scaling, we have obtained a numerical evidence for the occurrence of successive chiral-glass and spin-glass transitions at nonzero temperatures, T_{CG} > T_{SG} > 0. Hence, the spin and the chirality are decoupled in the ordering of the model. The chiral-glass exponents are estimated to be ν_{CG}=1.4+-0.2 and η_{CG}=0.6+-0.2, indicating that the chiral-glass transition lies in a universality class different from that of the Ising spin glass. The possibility that the spin and chiral sectors undergo a simultaneous Kosterlitz-Thouless-type transition is ruled out. The chiral-glass state turns out to be non-self-averaging, possibly accompanying a one-step-like peculiar replica-symmetry breaking. Implications to the chirality scenario of experimental spin-glass transitions are discussed.

cond-mat.dis-nn↗
arXiv2008

Spatiotemporal correlations of earthquakes in the continuum limit of the one-dimensional Burridge-Knopoff model

Spatiotemporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes, either with or without the viscosity term, are studied by means of numerical computer simulations. The continuum limit of the model is examined by systematically investigating the model properties with varying the block-size parameter a toward a\to 0. The Kelvin viscosity term is introduced so that the model dynamics possesses a sensible continuum limit. In the presence of the viscosity term, many of the properties of the original discrete BK model are kept qualitatively unchanged even in the continuum limit, although the size of minimum earthquake gets smaller as a gets smaller. One notable exception is the existence/non-existence of the doughnut-like quiescence prior to the mainshock. Although large events of the original discrete BK model accompany seismic acceleration together with a doughnut-like quiescence just before the mainshock, the spatial range of the doughnut-like quiescence becomes narrower as a gets smaller, and in the continuum limit, the doughnut-like quiescence might vanish altogether. The doughnut-like quiescence observed in the discrete BK model is then a phenomenon closely related to the short-length cut-off scale of the model.

cond-mat.other↗
arXiv2008

Simulation study of the two-dimensional Burridge-Knopoff model of earthquakes

Spatiotemporal correlations of the two-dimensional spring-block (Burridge-Knopoff) model of earthquakes are extensively studied by means of numerical computer simulations. The model is found to exhibit either ``subcritical'' or ``supercritical'' behavior, depending on the values of the model parameters. Transition between these regimes is either continuous or discontinuous. Seismic events in the ``subcritical'' regime and those in the ``supercritical'' regime at larger magnitudes exhibit universal scaling properties. In the ``supercritical'' regime, eminent spatiotemporal correlations, {\it e.g.}, remarkable growth of seismic activity preceding the mainshock, arise in earthquake occurrence, whereas such spatiotemporal correlations are significantly suppressed in the ``subcritical'' regime. Seismic activity is generically suppressed just before the mainshock in a close vicinity of the epicenter of the upcoming event while it remains to be active in the surroundings (the Mogi doughnut). It is also observed that, before and after the mainshock, the apparent $B$-value of the magnitude distribution decreases or increases in the ``supercritical'' or ``subcritical'' regimes, respectively. Such distinct precursory phenomena may open a way to the prediction of the upcoming large event.

cond-mat.other↗
arXiv2008

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

Spatiotemporal correlations of the two-dimensional spring-block (Burridge-Knopoff) models of earthquakes with the long-range inter-block interactions are extensively studied by means of numerical computer simulations. The long-range interaction derived from an elasticd theory, which takes account of the effect of the elastic body adjacent to the fault plane, falls off with distance r as 1/r^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\simeq 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, consistently with the observation. Large events often accompany foreshocks together with a doughnut-like quiescence as their precursors, while they hardly accompany aftershocks with almost negligible seismic correlations observed after the mainshock.

cond-mat.other↗
arXiv2008

Ordering of the pyrochlore Ising model with the long-range RKKY interaction

The ordering of the Ising model on a pyrochlore lattice interacting via the long-range RKKY interaction, which models a metallic pyrochlore magnet such as Pr_2Ir_2O_7, is studied by Monte Carlo simulations. Depending on the parameter k_F representing the Fermi wavevector, the model exhibits rich ordering behaviors.

cond-mat.stat-mech↗
arXiv2007

Non-linear rheology of layered systems - a phase model approach

We study non-linear rheology of a simple theoretical model developed to mimic layered systems such as lamellar structures under shear. In the present work we study a 2-dimensional version of the model which exhibits a Kosterlitz-Thouless transition in equilibrium at a critical temperature Tc. While the system behaves as Newtonain fluid at high temperatures T > Tc, it exhibits shear thinning at low temperatures T < Tc. The non-linear rheology in the present model is understood as due to motions of edge dislocations and resembles the non-linear transport phenomena in superconductors by vortex motions.

cond-mat.stat-mech↗
arXiv2007

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 $δ$-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.

cond-mat.other↗
arXiv2007

Vortex-induced topological transition of the bilinear-biquadratic Heisenberg antiferromagnet on the triangular lattice

The ordering of the classical Heisenberg antiferromagnet on the triangular lattice with the the bilinear-biquadratic interaction is studied by Monte Carlo simulations. It is shown that the model exhibits a topological phase transition at a finite-temperature driven by topologically stable vortices, while the spin correlation length remains finite even at and below the transition point. The relevant vortices could be of three different types, depending on the value of the biquadratic coupling. Implications to recent experiments on the triangular antiferromagnet NiGa$_2$S$_4$ is discussed.

cond-mat.stat-mech↗
arXiv2007

Rate- and State-Dependent Friction Law and Statistical Properties of Earthquakes

In order to clarify how the statistical properties of earthquakes depend on the constitutive law characterizing the stick-slip dynamics, we make an extensive numerical simulation of the one-dimensional spring-block model with the rate- and state-dependent friction law. Both the magnitude distribution and the recurrence-time distribution are studied with varying the constitutive parameters characterizing the model. While a continuous spectrum of seismic events from smaller to larger magnitudes is obtained, earthquakes described by this model turn out to possess pronounced ``characteristic'' features.

cond-mat.other↗
arXiv2006

Spin-chirality decoupling in Heisenberg spin glasses and related systems

Recent studies on the spin and the chirality orderings of the three-dimensional Heisenberg spin glass and related systems are reviewed with particular emphasis on the possible spin-chirality decoupling phenomena. Chirality scenario of real spin-glass transition and its experimental consequence on the ordering of Heisenberg-like spin glasses are discussed.

cond-mat.dis-nn↗
arXiv2006

Spin and chirality orderings of the one-dimensional Heisenberg spin glass with the long-range power-law interaction

The ordering of the one-dimensional Heisenberg spin glass interacting via the long-range power-law interaction is studied by Monte Carlo simulations. Particular attention is paid to the possible occurrence of the ``spin-chirality decoupling'' for appropriate values of the power-law exponent σ. Our result suggests that, for intermediate values of $σ$, the chiral-glass order occurs at finite temperatures while the standard spin-glass order occurs only at zero temperature.

cond-mat.dis-nn↗
arXiv2006

Novel ordering of the pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbor interaction

The ordering property of the classical pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbor interaction is investigated by means of a Monte Carlo simulation. The model is found to exhibit a first-order transition at a finite temperature into a peculiar ordered state. While the spin structure factor, i.e., the thermal average of the squared Fourier amplitude of the spin, exhibits a finite long-range order characterized by the commensurate spin order of the period four, the thermal average of the spin itself almost vanishes. It means that, although the amplitude of the spin Fourier component is long-range ordered, the associated phase degree of freedom remains to be fluctuating.

cond-mat.stat-mech↗
arXiv2006

Simulation Study of the One-Dimensional Burridge-Knopoff Model of Earthquakes

Spatio-temporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes are extensively studied by means of numerical computer simulations. Particular attention is paid to clarifying how the statistical properties of earthquakes depend on the frictional and elastic properties of earthquake faults. It is found that, as the velocity-weakening tendency of the friction force gets weaker, the system tends to be more critical, while, as the velocity-weakening tendency gets stronger, the system tends to be more off-critical with enhanced features of a characteristic earthquake. The model exhibits several eminent precursory phenomena prior to the large event in its spatio-temporal correlations. Preceding the mainshock, the frequency of smaller events is gradually enhanced, whereas, just before the mainshock, it is suppressed in a close vicinity of the epicenter of the upcoming event (the Mogi doughnut). The time scale of the onset of the doughnut-like quiescence depends on the extent of the frictional instability. Under certain conditions, preceding the mainshock, the apparent B-value of the magnitude distribution increases significantly. The existence of such distinct precursory phenomena may open a way to the prediction of the time and the position of the upcoming large event.

physics.geo-ph↗
arXiv2006

Spatiotemporal Correlations of Earthquakes

Statistical properties of earthquakes are studied both by the analysis of real earthquake catalog of Japan and by numerical computer simulations of the spring-block model in both one and two dimensions. Particular attention is paid to the spatiotemporal correlations of earthquakes, e.g., the recurrence-time distribution or the time evolution before and after the mainshock of seismic distribution functions, including the magnitude distribution and the spatial seismic distribution. Certain eminent features of the spatiotemporal correlations, e.g., foreshocks, aftershocks, swarms and doughnut-like seismic pattern, are discussed.

cond-mat.other↗
arXiv2005

Numerical study of the ordering of the +-J XY spin-glass ladder

The properties of the domain-wall energy and of the correlation length are studied numerically for the one-dimensional +-J XY spin glass on the two-leg ladder lattice, focusing on both the spin and the chirality degrees of freedom. Analytic results obtained by Ney-Niftle et al for the same model were confirmed for asymptotically large lattices, while the approach to the asymptotic limit is slow and sometimes even non-monotonic. Attention is called to the occurrence of the SO(2)-Z_2 decoupling and its masking in spin correlations, the latter reflecting the inequality between the SO(2) and Z_2 exponents. Discussion is given concerning the behaviors of the higher-dimensional models.

cond-mat.dis-nn↗
arXiv2005

Simulation study of spatio-temporal correlations of earthquakes as a stick-slip frictional instability

Spatio-temporal 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''

cond-mat.other↗
arXiv2004

Monte Carlo study of the ordering of the weakly anisotropic Heisenberg spin glass in magnetic fields

The ordering of the three-dimensional Heisenberg spin glass with the weak random anisotropy in magnetic fields is studied by extensive equilibrium Monte Carlo simulations. Both the spin and the chirality are monitored. We find strong numerical evidence that a replica symmetry breaking transition occurs in the chiral sector, which accompanies the simultaneous spin-glass order. Despite the similarity in the global symmetry, the ordering behavior of the weakly anisotropic Heisenberg spin glass differs significantly from that of the strongly anisotropic Ising spin glass. The obtained phase diagram in the temperature - magnetic field plane is similar to the experimental phase diagram. Our results highlight the importance of the chirality in the spin-glass ordering of the Heisenberg-like spin glass, and support the spin-chirality decoupling-recoupling scenario of spin-glass transitions.

cond-mat.dis-nn↗