arXiv subjects

Hikaru Kawamura

Publications and source records attributed to Hikaru Kawamura.

At least 55 records · Page 3Linked to original sources

arXiv2012

Statistical Physics of Fracture, Friction and Earthquake

We review the present status of our research and understanding regarding the dynamics and the statistical properties of earthquakes, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture, which provides a "microscopic" basis of our understanding of an earthquake instability, and on the statistical physical modelling of earthquakes, which provides "macroscopic" aspects of such phenomena. Recent numerical results on several representative models are reviewed, with attention to both their "critical" and "characteristic" properties. We highlight some of relevant notions and related issues, including the origin of power-laws often observed in statistical properties of earthquakes, apparently contrasting features of characteristic earthquakes or asperities, the nature of precursory phenomena and nucleation processes, the origin of slow earthquakes, etc.

cond-mat.stat-mech↗

arXiv2012

Ordering of the Heisenberg spin glass in four dimensions

Ordering of the Heisenberg spin glass in four dimensions (4D) with the nearest-neighbor Gaussian coupling is investigated by equilibrium Monte Carlo simulations, with particular attention to its spin and chiral orderings. It is found that the spin and the chirality order simultaneously with a common correlation-length exponent $ν_{CG}=ν_{SG}\simeq 1.0$, i.e., the absence of the spin-chirality decoupling in 4D. Yet, the spin-glass ordered state exhibits a nontrivial phase-space structure associated with a continuous one-step-like replica-symmetry breaking, different in nature from that of the Ising spin glass or of the mean-field spin glass. Comparison is made with the ordering of the Heisenberg spin glass in 3D, and with that of the 1D Heisenberg spin glass with a long-range power-law interaction. It is argued that the 4D might be close to the marginal dimension separating the spin-chirality decoupling/coupling regimes.

cond-mat.dis-nn↗

arXiv2012

Spin and chiral orderings of the antiferromagnetic XY model on the triangular lattice and their critical properties

We study the antiferromagnetic {\it XY} model on a triangular lattice by extensive Monte Carlo simulations, focusing on its ordering and critical properties. Our result clearly shows that two separate transitions occur at two distinct temperatures, the one at a higher temperature is associated with a $Z_2$-symmetry breaking driven by the chirality, and the one at a lower temperature is associated with the onset of the quasi-long-range order of the {\it XY} spin. We carefully examine the critical properties of each transition to find that the criticality of the chiral transition is consistent with the standard two-dimensional Ising universality class, whereas that of the spin transition might differ from the conventional Kosterlitz-Thouless (KT) one. The observed non-KT nature of the spin criticality is consistent with the most recent simulation result on the fully-frustrated {\it XY} model on a square lattice.

cond-mat.stat-mech↗

arXiv2011

Multiple-q states and 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 spin 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.

cond-mat.stat-mech↗

arXiv2011

Cubic and non-cubic multiple-q states in the Heisenberg antiferromagnet on the pyrochlore lattice

The ordering of the classical Heisenberg model on the pyrochlore lattice with the antiferromagnetic nearest-neighbor interaction J1 and the ferromagnetic next-nearest-neighbour interaction J2 is investigated by means of a mean-field analysis and a Monte Carlo simulation. For a moderate J2/J1-value, the model exhibits a first-order transition into an incommensurate multiple-q ordered state where multiple Bragg peaks coexist in the spin structure factor. We show that there are two types of metastable multiple-q states, a cubic symmetric sextuple-q state and a non-cubic symmetric quadruple-q state. Based on a Monte Carlo simulation, we find that the cubic sextuple-q state appears just below the first-order transition temperature, while another transition from the cubic sextuple-q state to the non-cubic quadruple-q state occurs at a lower temperature.

cond-mat.stat-mech↗

arXiv2011

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 to experiments are discussed.

cond-mat.dis-nn↗

arXiv2011

Z2-vortex order of frustrated Heisenberg antiferromagnets in two dimensions

We discuss the recent experimental data on various frustrated quasi-two-dimensional Heisenberg antiferromagnets from the viewpoint of the Z2-vortex order, which include S=3/2 triangular-lattice antiferromagnet NaCrO2, S=1 triangular-lattice antiferromagnet NiGa2S4, S=1/2 organic triangular-lattice antiferromagnets κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, and S=1/2 kagome-lattice antiferromagnet volborthite Cu3V2O7(OH)22H2O, etc.

cond-mat.mtrl-sci↗

arXiv2010

Novel spin-liquid states in the frustrated Heisenberg antiferromagnet on the honeycomb lattice

Recent experiment on a honeycomb-lattice Heisenberg antiferromagnet (AF) Bi$_3$Mn$_4$O$_{12}$(NO$_3$) revealed a novel spin-liquid-like behavior down to low temperature, which was ascribed to the frustration effect due to the competition between the AF nearest- and next-nearest-neighbor interactions $J_1$ and $J_2$. Motivated by the experiment, we study the ordering of the $J_1$ -$J_2$ frustrated classical Heisenberg AF on a honeycomb lattice both by a low-temperature expansion and a Monte Carlo simulation. The model has been known to possess a massive degeneracy of the ground state, which, however, might be lifted due to thermal fluctuations leading to a unique ordered state, the effect known as 'order-by-disorder'. We find that the model exhibits an intriguing ordering behavior, particularly near the AF phase boundary. The energy scale of the order-by-disorder is suppressed there down to extremely low temperatures, giving rise to exotic spin-liquid states like a "ring-liquid" or a "pancake-liquid" state accompanied by the characteristic spin structure factor and the field-induced antiferromagnetism. We argue that the recent experimental data are explicable if the system is in such exotic spin-liquid states.

cond-mat.str-el↗

arXiv2010

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.

cond-mat.stat-mech↗

arXiv2010

Signature of a Z_2 vortex in the dynamical correlations of the triangular-lattice Heisenberg antiferromagnet

Dynamical properties of the classical Heisenberg antiferromagnet on the triangular lattice are investigated by means of a spin-dynamics simulation and an analytical calculation. While the model was suggested to exhibit a topological transition driven by the Z_2-vortex binding-unbinding, weakness of the associated thermodynamic singularity has made it difficult to observe the evidence of the Z_2 vortex experimentally so far, only some indirect support. Here, we show that the signature of the Z_2-vortex excitation and the vortex-induced topological transition can be captured from the dynamical spin correlations. In particular, the dynamical spin structure factor exhibits a characteristic central peak around the Z_2-vortex transition, and this central peak will be a fingerprint of the Z_2-vortex excitation.

cond-mat.stat-mech↗

arXiv2010

Simulation study of the inhomogeneous Olami-Feder-Christensen model of earthquakes

Statistical properties of the inhomogeneous version of the Olami-Feder-Christensen (OFC) model of earthquakes is investigated by numerical simulations. The spatial inhomogeneity is assumed to be dynamical. Critical features found in the original homogeneous OFC model, e.g., the Gutenberg-Richter law and the Omori law are often weakened or suppressed in the presence of inhomogeneity, whereas the characteristic features found in the original homogeneous OFC model, e.g., the near-periodic recurrence of large events and the asperity-like phenomena persist.

cond-mat.stat-mech↗

arXiv2010

Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions

The nature of the ordering of the one-dimensional Heisenberg spin-glass model with a long-range power-law interaction is studied by extensive Monte Carlo simulations, with particular attention to the issue of the spin-chirality decoupling/coupling. Large system sizes up to $L=4096$ are studied. With varying the exponent $σ$ describing the power-law interaction, we observe three distinct types of ordering regimes. For smaller $σ$, the spin and the chirality order at a common finite temperature with a common correlation-length exponent, exhibiting the standard spin-chirality coupling behavior. For intermediate $σ$, the chirality orders at a temperature higher than the spin, exhibiting the spin-chirality decoupling behavior. For larger $σ$, both the spin and the chirality order at zero temperature. We construct a phase diagram in the $σ$ versus the temperature plane, and discuss implications of the results. Critical properties associated with both the chiral-glass and the spin-glass transitions are also determined.

cond-mat.dis-nn↗

arXiv2010

Spin-chirality decoupling and critical properties of a two-dimensional fully frustrated XY model

We study the ordering of the spin and the chirality in the fully frustrated XY model on a square lattice by extensive Monte Carlo simulations. Our results indicate unambiguously that the spin and the chirality exhibit separate phase transitions at two distinct temperatures, i. e. , the occurrence of the spin-chirality decoupling. The chirality exhibits a long-range order at T_c=0.45324(1) via a second-order phase transition, where the spin remains disordered with a finite correlation length ξ_s(T_c) \sim 120. The critical properties of the chiral transition determined from a finite-size scaling analysis for large enough systems of linear size L > ξ_s(T_c) are well compatible with the Ising universality. On the other hand, the spin exhibits a phase transition at a lower temperature T_s=0.4418(5) into the quasi-long-range-ordered phase. We found η(T_s)=0.201(1), suggesting that the universality of the spin transition is different from that of the conventional Kosterlitz-Thouless (KT) transition.

cond-mat.stat-mech↗

arXiv2010

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/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 is discussed.

cond-mat.dis-nn↗

arXiv2010

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 exhibits ``asperity''-like phenomena, {\it i.e.}, the same region ruptures many times near periodically [T.Kotani {\it et al}, Phys. Rev. E {\bf 77}, 010102 (2008)]. Such periodic or characteristic features apparently coexist with power-law-like critical features, {\it 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.

cond-mat.stat-mech↗

arXiv2010

Chirality scenario of the spin-glass ordering

Detailed account is given of the chirality scenario of experimental spin-glass transitions. In this scenario, the spin glass order of weakly anisotropic Heisenberg-like spin-glass magnets including canonical spin glasses are essentially chirality driven. Recent numerical and experimental results are discussed in conjunction with this scenario.

cond-mat.dis-nn↗

arXiv2010

Z_2-vortex ordering of the triangular-lattice Heisenberg antiferromagnet

Ordering of the classical Heisenberg antiferromagnet on the triangular lattice is studied by means of a mean-field calculation, a scaling argument and a Monte Carlo simulation, with special attention to its vortex degree of freedom. The model exhibits a thermodynamic transition driven by the Z_2-vortex binding-unbinding, at which various thermodynamic quantities exhibit an essential singularity. The low-temperature state is a "spin-gel" state with a long but finite spin correlation length where the ergodicity is broken topologically. Implications to recent experiments on triangular-lattice Heisenberg antiferromagnets are discussed.

cond-mat.stat-mech↗

arXiv2010

Two models of spin glasses -- Ising versus Heisenberg

Brief review is given on recent numerical research of the ordering of two typical models of spin glasses (SGs), the three-dimensional (3D) Ising SG and the 3D Heisenberg SG models. Particular attention is paid to the questions of whether there is a thermodynamic transition in zero field, what are the associated critical properties, what is the nature of the ordered state, particularly of a possible replica-symmetry breaking, and whether there is a thermodynamic transition in applied fields. The properties of the two models are contrasted, and possible relation to experiments is discussed.

cond-mat.dis-nn↗