Yoshitake Yamazaki

The cross-over exponent up to ϵ3 (ϵ=4−d) by using Callan-Symanzik equations

Abstract By means of Callan-Symanzik equations, the cross-over exponent φ is derived up to ϵ 3 ( ϵ =4− d ) in the Wilsons N -component spin systems.

On the critical dynamics of extended-impurity systems in cubic anisotropic crystals

Critical dynamics is studied for N-component spin systems in cubic anisotropic crystals in the presence of extended impurities, namely ed-dimensionally connected impurities distributed randomly in d∼ (≡ d − ed) dimensions (d: dimensionality of the medium; d ≡ 4 - e). As extended impurities make the systems coordinate-anisotropic, new results are expected in the critical dynamics. By means of a field-theoretic renormalization-group (RG) approach, critical regions and dynamic critical exponents are evaluated, to the lowest order in a double e, ed expansion, for models corresponding to model A, model B and model C, proposed by Hohenberg and Halperin.

Critical exponent η of isotropic spin systems with long and short-range interactions

Abstract Critical phenomena, in particular, the critical exponent η, in isotropic N -component spin systems with long and short range interactions are discussed in the regions of the weakly long-range, the intermediate-range, and the long-range potentials. The expressions for η in these three regions are derived and their stability is discussed.

Lattice Green's Function for the Orthorhombic Lattice in Terms of the Complete Elliptic Integral

The real and imaginary parts of the orthorhombic lattice Greens function at the origin are expressed as a sum of simple integrals of the complete elliptic integrals of the first kind. In order to give the expressions for all values of the variable from − ∞ to + ∞, use is made of the method of analytic continuation. The results of the numerical computations are shown by figures.

Static and dynamic properties of XY systems with extended defects in cubic anisotropic crystallines

Static and dynamic critical behavior ofXY systems in cubic anisotropic crystallines, with extended defects (or quenched nonmagnetic impurities) strongly correlated alongɛd-dimensional space and randomly distributed ind − ɛd dimensions, were studied. These extended defects make the systems coordinate anisotropic, resulting in unique critical behavior due to competition between the cubic anisotropy and the coordinate anisotropy. The systems were analyzed by anɛ1/2 (ɛ≡4 − d) type of expansion with double expansion parameters based on a renormalization-group (RG) approach. Critical exponents were calculated near the second-order phase transition point and the behavior of the first-order transition was evaluated near the tricritical point.

Critical behavior in random-spin systems with long-range interactions

Effects of the potential range of the interaction to critical behaviors of quenched random-spin systems are investigated in the limit M → 0 of the MN-component models by means of the renormalization-group theories. As static critical phenomena the stability of the fixed points is investigated and the critical exponents (η, γ, α, crossover index) and the equation of state are derived. These phenomena are different from those in pure systems, for the positive specific heat exponent α of the pure Heisenberg system.

Racemic and chiral structures of banana-shaped smectic liquid crystals viewed as one-dimensional piezoelectric crystals

A smectic liquid-crystal phase formed by achiral banana-shaped molecules (C-B2) is studied as one-dimensional piezoelectric crystals with fluidity of tilted-C-2V anisotropy in the other two spatial dimensions. Variation of the elastic-piezoelectric free energy of the system predicts the existence of racemic (R), left-, and right-handed chiral (H) antiferroelectric equilibrium structures, a result in agreement with the observation by Link [Science 278, 1924 (1997)]. The electric-field-induced ferroelectric state is shown to be a special C-2 symmetry, which confirms the measurements by optical second harmonic generation in a C-B2 by Macdonald [Phys. Rev. Lett. 81, 4408 (1998)]. The hysteresis loop of switching polarization is also discussed, and the molecular tilt angle dependence of spontaneous polarization is obtained as a function of the elastic and the piezoelectric constants

Adaptive–intelligent control by neural‐net systems

Adaptive–intelligent control by neural‐net systems is discussed. Actual adaptive–intelligent control is realized in a general system through the following two hierarchical steps: (1) choosing a hierarchical coordinate system (associated with the environment of the system) and constructing the hierarchical evaluation functions (specifying its control states) and (2) finding a set of the most appropriate hierarchical values for the control parameters (giving the minimum value to the evaluation function). Step 1 establishes “intelligently self‐controllable (thinking) algorithms” with human‐like intelligence for various events (concepts). Step 2 studies the intelligently self‐controllable (thinking) algorithms for finding the most appropriate state. Adaptive–intelligent control by neural‐net systems is realized by integrating both intelligently self‐controllable (thinking) algorithms on the neural‐net systems. Here step 2 is mainly discussed in the neural‐net systems of Boltzmann type machines using the method of stochastic dynamics.

Critical behavior of N-component spin systems with random impurities in cubic-anisotropy crystalline material

Static and dynamic critical behavior of N-component spin systems with cubic anisotropy and with quenched random impurities are studied in the limit ed→0+ of the impurity system whose impurities are strongly correlated in ed dimensions while they are randomly distributed in the remaining d − ed dimensions. By means of the renormalization-group approach, the stability of the fixed points, the flow of the interactions and the critical exponents are evaluated up to two-loop order. The behavior of the first order phase transition to appear is also studied.

Critical behaviour of two-component spin systems with quenched random nonmagnetic impurities in cubic anisotropic crystals

By means of the renormalisation-group approach, static and dynamic critical behaviours are studied for the XY spin system with cubic anisotropy and with quenched random nonmagnetic impurities. The stability of the quenched-random-impurity fixed point in d ( identical to 4- epsilon ) dimensions, the flow diagram of the interactions and the critical exponents are investigated, within the two-loop approximation, in terms of the epsilon 1/2 expansion. It is shown that the transition that appears is a first-order transition.