World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms — the loop algorithm, the worm algorithm, and the directed-loop algorithm — for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.

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We investigate the vibrational structure of electronic spectra for the transition from the nondegenerate A state to E states in E_g⊗e_g Jahn–Teller systems with the trigonal field included. By extending the analysis by Longuet-Higgins et al. [Proc. R. Soc. London, Ser. A 244 (1958) 1] to this classically chaotic system, we find that the triple-humped structure is manifest with increasing anharmonicity. Such a structure cannot be derived using the semiclassical Franck–Condon (FC) approximation, and is caused by the chaos-induced breaking of the FC principle.

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The plane-Poiseuille-type flow is numerically investigated in a rotating coordinate system with small system rotation rates for low Reynolds numbers. We obtained two-dimensional and three-dimensional solutions which exhibit characteristic coherent vortical structures by time-evolution calculations of the Fourier and Chebyshev expansions. It is interesting that mean-absolute-vorticity becomes nearly zero in the region where the vortical structures concentrate. We found for relatively small Reynolds number and rotation number ranges that two-dimensional solutions and traveling-wave solutions having the same spatial symmetry are stably maintained. We also found a two-dimensional periodic solution which switches two and four vortices states. The asymptotic states of the time-developing solutions are obtained as steady or traveling-wave solutions by the Newton–Raphson iteration method.

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The phase transition in (CH₃)₃NCH₂COO·H₃PO₄ at T_C1=365 K was studied by ³¹P-NMR. Spin–lattice relaxation time shows a sharp dip at T_C1 due to the critical slowing down. The critical relaxation rate is reproduced by the quasi-one-dimensional Ising model with antiferroelectric interactions along both the intrachain and interchain directions. The interaction parameters for intrachain J_|| and interchain J_⊥ are determined to be 693(3) and 4.1(1) K, respectively.

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Electron transport is investigated theoretically for an electron which is coupled to a localized spin system. The dc electrical conductivity of spin-fermion models in one dimension is studied by the direct numerical estimation of the Kubo formula. The dependence of the conductivity on temperature and external magnetic field is investigated. When the localized spins are antiferromagnetically coupled on a chain, the conductivity shows a monotonic increase with magnetic field, which is ordinary magnetoresistance. However, in a system where the localized spins form an antiferromagnetically coupled two-leg ladder, the conductivity shows an anomalous non-monotonic field dependence. Analysis of the spin configuration of the localized spin system reveals that quantum fluctuation determines the conductivity through a dimerized-rung spin configuration, and the formation of local triplets on the ladder rungs causes the decrease in conductivity.

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The conductance of disordered wires with symplectic symmetry is studied by the supersymmetric field theory. Special attention is focused on the case where the number of conducting channels is odd. Such a situation can be realized in metallic carbon nanotubes. The average dimensionless conductance ⟨g⟩ is obtained using Zirnbauer’s super-Fourier analysis. It is shown that with increasing wire length, ⟨g⟩→1 in the odd-channel case, while ⟨g⟩→0 in the ordinary even-channel case. It should be emphasized that the so-called Zirnbauer’s zero mode, which has been believed to be unphysical, is essential for describing the anomalous behavior in the odd-channel case.

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We investigate the superconductivity in the deuterated BEDT-TTF molecular substitution system κ-[(h8-BEDT-TTF)_1−x(d8-BEDT-TTF)_x]₂Cu[N(CN)₂]Br, where h8 and d8 denote fully hydrogenated and deuterated molecules, respectively. Systematic and wide-range (x=0–1) substitution can accurately control chemical pressure near the Mott boundary, which results in the modification of the superconductivity. After cooling slowly, an increase in T_c observed up to x∼0.1 is evidently caused by the chemical pressure effect. Neither a reduction of T_c nor a suppression of superconducting volume fraction is found below x∼0.5. This demonstrates that the effect of disorder by substitution is negligible in the present system. With further increase in x, both T_c and superconducting volume fraction start to decrease toward values at x=1.

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Magnetic excitations in a single crystal of heavy-fermion superconductor PrOs₄Sb₁₂ have been studied by inelastic neutron scattering (INS) at low temperatures under high magnetic fields. The crystal field (CF) excitations at 0.7 meV observed in a previous INS study of a polycrystal sample were confirmed in this study on a single crystal. The observed excitations in the zero magnetic field soften around a wave vector (1,0,0), which is the modulation vector of the field-induced antiferro-quadrupolar ordering, suggesting the presence of quadrupolar instability. The observed field dependence of excitations is better reproduced in a singlet ground-state model rather than in a non-Kramers doublet ground-state model. In a high resolution experiment, furthermore, the change of the excitation spectra at (1,0,0) was observed on passing through the superconducting transition temperature, indicating that the excitation and the superconductivity are closely related in PrOs₄Sb₁₂.

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The effect of a small amount of substitution on magnetic ordering in a frustrated triangular lattice antiferromagnet CuFeO₂ has been studied by neutron diffraction, magnetic susceptibility and specific heat measurements on CuFe_1−xAl_xO₂ single-crystals with x=0.02 and x=0.05. With only a small amount of substitution, x=0.02, the zero-field successive magnetic phase transitions with quasi-Ising character observed for x=0.00 are entirely changed to successive phase transitions from a paramagnetic state to an incommensurate complex state through an incommensurate magnetic state, suggesting that the original Heisenberg spin character hidden in CuFeO₂ is retrieved.

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Under the hydrostatic pressure P=1.48 GPa, polarized neutron elastic scattering experiments have been carried out on the coupled spin dimer system TlCuCl₃ with the gapped ground state at ambient pressure. Pressure-induced magnetic ordering occurs at the transition temperature T_N=16.9 K. As in the field-induced and impurity-induced magnetic ordered phases, the ordered moments lie in the a–c plane just below T_N. An additional spin reorientation (SR) phase transition was observed at T_SR=10 K, where the ordered moments start to incline toward the b-axis. The temperature variations of the direction and the magnitude of the ordered moments were also investigated.

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YbGaGe was reported as the first example of a material with zero thermal expansion that is accomplished by the temperature-variant Yb²⁺/Yb³⁺ configuration [Salvador et al.: Nature 425 (2003) 702]. Here we report magnetic, transport, X-ray diffraction and thermal expansion measurements of single-crystal samples. The results reveal a stable divalent state of Yb ions in YbGaGe and a distinct volume-thermal contraction with decreasing temperature.

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Nuclear spin–lattice relaxation in one-dimensional Heisenberg ferrimagnets is studied in terms of a modified spin-wave theory. We consider the second-order process, where a nuclear spin flip induces virtual spin waves which are then scattered thermally via the four-magnon exchange interaction, as well as the first-order process, where a nuclear spin directly interacts with spin waves via the hyperfine interaction. We point out a possibility of the three-magnon relaxation process predominating over the Raman one and suggest model experiments.

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Recently the Preissman scheme has become very popular [Zao and Qin: J. Phys. A 33 (2000) 3613; Chen: Appl. Math. Comput. 124 (2001) 371; Reich: Reading Material of Int. Workshop on Structure-Preserving Algorithms, 2001, Vol. 6, No. 3, pp. 153–174; Wang and Qin: Math. Comput. Model. 36 (2002) 963] since it was found to be a multisymplectic scheme [Bridges: Math. Proc. Cambridge Philos. Soc. 121 (1997) 147]. However, When it is applied to solve the periodic boundary problem of the soliton equations with degenerate lagrangian like the Korteweg–De Vries equation, the Kadomtsev–Petviashvili equation and the water waves equations, the general widely-used iterative method refereed as the simple iterative method [Wineberg et al.: J. Comput. Phys. 97 (1991) 311] is not convergent, so are the other iterative method such as Newton method and conjugate gradient method. Why? This problem has puzzled researchers all along. In this paper, taking the KdV equation as an example, we analyze this problem and show that the unconvergence is due to indeterminacy of the introduced potential function. An artificial numerical condition is added to the periodic boundary condition. The added boundary condition makes the numerical implementation of the multisymplectic Preissman scheme practical and is proved not to change the primary numerical solutions of the KdV equation. Numerical experiments on soliton collisions, with comparisons of the spectral method and the Zabusky–Kruskal scheme, are also provided to confirm our conclusion and show the merits of the multisymplectic scheme.

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The classical and nonclassical Lie group approaches are extended and applied to construct new conditional similarity reductions for nonlinear systems. The application of the method to a simple (2+1)-dimensional KdV equation results in not only the known conditional similarity reductions obtained by the modified Clarkson and Kruskal’s direct method but also a great diversity of classical and nonclassical conditional similarity reductions.

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Quantum non-integrable systems have pseudochaos in the phase of the eigenfunctions. In particular, correlation function of wave functions at two different points disappears, when observation process, which requires space and/or time average over a small range, is taken into account. This gives rise to the realization of decoherence in measuring processes. By virtue of this property of quantum chaos, various problems and paradoxes are explained in the framework of conventional quantum mechanics. The subjects treated here are the duality of wave and particle, the wave function collapse in measurement, Stern–Gerlach experiments, Schrödinger’s cat paradox, the Einstein–Podolsky–Rosen paradox and quantum Zeno effect.

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An improved algorithm is proposed for Monte Carlo methods to study fermion systems interacting with adiabatical fields. To obtain a weight for each Monte Carlo sample with a fixed configuration of adiabatical fields, a series expansion using Chebyshev polynomials is applied. By introducing truncations of matrix operations in a systematic and controlled way, it is shown that the cpu time is reduced from O(N³) to O(N) where N is the system size. Benchmark results show that the implementation of the algorithm makes it possible to perform systematic investigations of critical phenomena using system-size scalings even for an electronic model in three dimensions, within a realistic cpu timescale.

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We derive the exact ground-state energy of the one-dimensional Ising model in random fields taking values h, 0 and −h with general probabilities. The random-field Ising model on a ladder is also analyzed by showing its equivalence to the random-field Ising chain with field values ±h and 0 for h<J. The zero-temperature transfer matrix is used to obtain the results.

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We investigated the asymptotic probability distribution function of the longitudinal velocity increment in incompressible three-dimensional turbulence. According to the observation on the large Reynolds number atmospheric flow by Praskovsky and Oncley [Phys. Rev. Lett. 73 (1994) 3399] the distribution is of exponential type in the inertial region, whose slope decreases as the separation decreases. This simple nature was examined with the aid of the forced large-scale simulation with R_λ=380 on 1024³ meshes, where a certain embryo of the exponential distribution is found. The deduced asymptotic distribution function agrees quantitatively with the observed pdf by those authors. A possible reason for the exponential distribution is theoretically considered based on the conditional average method.

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The unsteady motion of an incompressible viscous conducting fluid with embedded small inert spherical particles in a channel bounded by two rigid, non-conducting,infinite parallel plates in presence of an external magnetic field acting transversely to the plates has been discussed in this paper. The flow is supposed to generate impulsively from rest due to rectified sine pulses applied periodically on the upper plate with the lower plate held fixed. There is no external electric field imposed on the system and the magnetic Reynolds number is very small. Exact solution of the problem is obtained by the method of Fourier analysis. The inquiries are made about the fluid and the particle velocities and the skin-frictions at the walls. The effects of the magnetic field and the particles on the fluid velocity and the skin-frictions at the walls are examined quantitatively. Finally, the solution for the fluid velocity derived by the present method has been compared with that obtained by the usual method of Laplace transforms and confirms that both the results are same.

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We have measured the elastic constants of PrNi₅, which has a singlet ground state, Γ₄, as a function of the temperature. The characteristic anomalies have been observed around 23 K in longitudinal C₁₁ and C₃₃. The minimum temperature of C₁₁ and C₃₃ are higher than calculated results only with quadrupolar interactions. Therefore, we have used a magnetoelastic Hamiltonian with coupling of strains and higher-order multipoles in analysis. In C₁₁ and C₃₃, the anomalies can be explained by the strain susceptibilities, which include the multipolar operators O₆⁰ and O_xy⁴.

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For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the essential character of the Hamiltonian within a limited number of basis set. Its validation is confirmed by the convergence property of the density matrix within the subspace. The following quantities are calculated; energy, force, density of states, and energy spectrum. Molecular dynamics simulation of Si(001) surface reconstruction is examined as an example, and the results reproduce the mechanism of asymmetric surface dimer.

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Current–voltage characteristics are measured in the quasi-two dimensional organic conductor α-(BEDT-TTF)₂KHg(SCN)₄ at temperatures down to 0.5 K and in the magnetic field up to 25 T. The non-linear conduction with a threshold electric field is found in the density wave state. The features of threshold electric field obtained in the low magnetic field region are explained by the unconventional charge density wave model. In the high magnetic field region, where the Shubnikov–de Haas oscillations appear, the current–voltage characteristics reveal that the density wave state synchronizes with the filling of the electron on the Landau level and continues even above a kink field 23 T.

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Thallium monosulfide, TlS, contains Tl¹⁺ and Tl³⁺ ions and is classified as a mixed valence compound. TlS is also known to crystallize into two different structures, chain type tetragonal structure and layer type monoclinic structure. In this study, electronic structures of the tetragonal and monoclinic TlS have been studied using linear-muffin-tin-orbital (LMTO) calculations. The calculated band dispersions show that tetragonal TlS has an indirect gap from T(2π⁄a,0,0) to W(π⁄a,π⁄a,π⁄c), and that monoclinic TlS has a direct gap at Γ. For both crystals, the main valence bands are composed of two parts. The lower valence bands are derived from Tl 6s–S 3p bonding states, while the upper valence bands are derived mainly from S 3p states. The top of the valence bands has some character of the Tl¹⁺ 6s–S 3p antibonding state. For monoclinic TlS, the microscopic mechanism of the structural phase transition is argued in terms of the present band results. The calculated densities of states (DOS’s) are also compared with previously reported photoemission data.

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We consider the effect of microwave radiation on the dissipative and Hall components of the conductivity and resistivity tensors in two-dimension electron systems. It is shown that photon-assisted impurity scattering of electrons can result in oscillatory dependences of both dissipative and Hall components of the conductivity and resistivity tensors on the ratio of radiation frequency to cyclotron frequency. The Hall conductivity and resistivity can include a component induced by microwave radiation which is an even function of the magnetic field. The phase of the dissipative resistivity oscillations and the polarization dependence of their amplitude are compared with those of the Hall resistivity oscillations. The developed model can clarify the results of recent experimental observations of the radiation induced Hall effect.

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We have carried out the X-ray photoemission study of dodecanethiolate-(DT-) passivated Ag nanoparticles supported on the highly oriented pyrolytic graphite (HOPG) substrates. From detailed line-shape analyses of Ag 3d core-level photoemission spectra of DT-passivated Ag nanoparticles, it is found that Ag 3d core-level spectra consist of the two components. We attribute these components to the inner Ag atoms and surface Ag atoms bonded to surface dodecanethiolates. Furthermore, we have investigated the nanoparticle-diameter-dependent valence-band photoemission spectra. From these results, we discuss the electronic properties of DT-passivated Ag nanoparticles.

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Intensive high-field ESR studies have been performed to investigate the peculiar ground state of a quasi-one dimensional cupric oxide Ca_1−xCuO₂ (x=0.164), to which a two-sublattice model (chain-dimer model) composed of a Heisenberg antiferromagnetic chain and dimer state with low spin density is proposed from the results of magnetic susceptibility and specific heat measurements. Using the powder sample and high frequency sources from 60 to 490 GHz, we observed antiferromagnetic resonance mode with a typical frequency–field relation of the easy-axis type at 1.8 K. Moreover, weak ESR signals are also observed in the ordered state. From the analysis of the integrated intensity for those weak signals, it is found that the dimer model reproduces the temperature dependent behaviors quite well. These results support the chain-dimer model from the microscopic point of view.

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In order to elucidate quadrupolar and magnetic interactions in the antiferroquadrupolar (AFQ) and antiferromagnetic (AFM) ordering compound DyB₂C₂, neutron diffraction experiments were performed on powdered and single-crystalline samples in addition to reexamination of specific heat and magnetization properties on the Y-diluted system Dy_1−xY_xB₂C₂. The results suggest that there is a percolation threshold at x=0.4–0.5 for the AFQ ordering. The broadening behavior of magnetic reflection peaks by the Y dilution suggests that the AFQ interaction is probably pseudo-one-dimensional with strong AFQ interactions along the c-axis and weak ferroquadrupolar interactions in the c-plane.

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In an adiabatic approximation we propose a theoretical method which combines the thermal coherent state with a quantum procedure to study temperature dependence of the magnetic excited gap in the spin–Peierls chain with frustration based on the bosonized continuum Hamiltonian. In terms of the thermal coherent state the magnetic excitations at finite temperature can be viewed as the coherent excitations on an incoherent background constituted by the quasiparticles in thermal equilibrium. The formulations of the magnetic excited gap as a function of temperature are obtained analytically by solving a set of coupled equations. As an example, this method is applied to the spin–Peierls compound CuGeO₃. It is shown that our theoretical results are well consistent with the inelastic neutron scattering experimental data for CuGeO₃ in the normalized plane consisted of gap and temperature.

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The minor hysteresis loops were measured with increasing magnetic field amplitude H_a step by step and analyzed in Fe single crystal, polycrystalline metals and A533B steel. We have defined several new magnetic properties in the minor loops: they are pseudo magnetization B_a^*, pseudo coercive force H_c^*, pseudo remanence B_R^*, pseudo hysteresis loss W_F^*, pseudo remanence work W_R^*, and three pseudo magnetic susceptibilities χ_H^*, χ_R^* and χ_a^*. H_c^* is the magnetic field where the magnetization becomes zero in the minor loop. We found three relations of H_c^*⁄H_a=1⁄2, B_R^*⁄B_a^*=3⁄4 and W_R^*⁄W_F^*=1⁄6 in a limited range of H_a and they are independent of H_a as well as the kind of samples. Then we can obtain a simple product rule of 8B_R^*H_c^*=3B_a^*H_a. Domain wall potential is used to explain the magnetic phenomena. The height of crests and the depth of troughs depend on the grain size, precipitates and dislocation density. The relations between pseudo properties, W_R^*–B_R^*, W_F^*–B_a^*, H_c^*–B_R^*, H_c^*–1⁄χ_H^*, 1⁄χ_R^*–B_R^* and 1⁄χ_a^*–B_a^* are analyzed and simple formulas about the potential structure are obtained. We found four constants and six coefficients. The coefficients increase or decrease with the grain size of polycrystalline metals.

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We construct a microscopic Hamiltonian for the ferromagnetism of UGe₂ by taking account of the orbital degeneracy of the 5-f electrons and investigate possible phases by the Hartree–Fock approximation. We reduce the number of mean values to be determined by assuming the magnetic orders where the coplanar magnetic moments perpendicular to the c-axis constitute an a-axis moment as a whole. Because of the orbital degeneracy, the anisotropies of the crystalline electric field term and the hopping term competes with each other. Moreover occupation number in each atomic orbit is sensitive to the relation between the crystalline electric field and the Coulomb interaction. In consequence, a rich ground state phase diagram with various different ferromagnetic orders is obtained.

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The magnetization plateaux in two dimensionally coupled S=1⁄2 dimerized zigzag Heisenberg chains are investigated by means of the bond operator mean field approximation. In the absence of the interchain coupling, this model is known to have a plateau at half of the saturation magnetization accompanied by the spontaneous translational symmetry breakdown. The parameter regime in which the plateau appears is reproduced well within the present approximation. In the presence of the interchain coupling, this plateau is shown to be suppressed. This result is also supported by the numerical diagonalization calculation.

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Magnetic ordering around the ferroelectric transition temperature T_C1 of weakly ferroelectric YMn₂O₅ has been reinvestigated by single-crystal neutron diffraction and dielectric measurements. Besides a two-dimensionally modulated incommensurate magnetic (2D-ICM) phase with the propagation vector q=(q_x,0,q_z) and a lock-in commensurate magnetic (CM) one with q=(\\frac12,0,\\frac14) reported previously, we observed a 1D-ICM phase characterized by q=(q_x,0,\\frac14) with q_x∼0.492 that appears in a narrow temperature interval of ∼1 K and separates the 2D-ICM and CM phases. Corresponding to the 2D-ICM-to-1D-ICM and 1D-ICM-to-CM phase transitions at T=40.8 K and 40.0 K, a sharp peak and a shoulder in the dielectric constant along the b-axis were detected. These results suggest that the ferroelectricity appears simultaneously with the magnetic phase transition from the 2D-ICM to 1D-ICM phase in YMn₂O₅.

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Magnetic interactions in the nanoscale ferrimagnetic ring [Mn(hfac)₂NITPh]₆ abbreviated as Mn₆R₆ are estimated by comparing experimental data with our numerical data as obtained from the exact diagonalization of a Heisenberg model. Our results suggest that next nearest neighbor radical–radical interactions are essential to reproduce the magnetic structure of Mn₆R₆ well. The existence of these interactions means that Mn₆R₆ is a kind of frustrated spin cluster. We predict that the field derivative of magnetization should have two peaks in the range of magnetic field 380–420 T, which is beyond the range of current experimental observations. We also find that the local spin density of the frustrated model shows a different behavior from those of non-frustrated models studied in preceding works.

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We consider S=1⁄2 antiferromagnetic Heisenberg chains with alternating bonds and quenched disorder, which represents a theoretical model of the compound CuCl_2xBr_2(1−x)(γ-pic)₂. Using a numerical implementation of the strong disorder renormalization group method we study the low-energy properties of the system as a function of the concentration, x, and the type of correlations in the disorder. For perfect correlation of disorder the system is in the random dimer (Griffiths) phase having a concentration dependent dynamical exponent. For weak or vanishing disorder correlations the system is in the random singlet phase, in which the dynamical exponent is formally infinity. We discuss consequences of our results for the experimentally measured low-temperature susceptibility of CuCl_2xBr_2(1−x)(γ-pic)₂.

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