Showing papers in "Progress of Theoretical Physics in 1966"

Number-Phase Fluctuations in Two-Band Superconductors

Abstract: It is shown that in a clean two-band (transition-metal) superconductor there appears a collective excitation corresponding to small fluctuations of th~ relative phase of the two "condensates". In contrast to the transverse collective excitations in ordinary superconduc­ tors, the energy of this mode can be derived directly from existing experimental data ; for Nb it lies about at the middle of the smaller single-particle gap. Direct experimental detec­ tion of this resonance is estimated to be rather beyond the limits of available techniques, but its effect on th~ ultrasound dispersion curve should be easily observable. The pheno­ menon is used to elucidate the physical nature of excitons in superconductors in general.

Baryon Number Changing Currents

Abstract: An attempt is made to generalize the algebra of currents by inclusion of baryon number changing currents which connect baryons and mesons. In this algebra both baryons and mesons are grouped together in a representation, i.e. in a supermultiplet. The currents are constructed from a set of fundamental particles consisting of a spinor SU(3) triplet and a scalar triplet. Most of the important hadrons are included in a supermultiplet but the baryon decimet is not. The hadrons discussed here correspond to bare hadrons without the Yukawa interactions. Mass relations, cross sections and other consequences obtained from this symmetry scheme are discussed.

Magnetization Process in an Ising Spin System

Abstract: total number of negative spins and the numbers of interaction lines connecting either two negative spins or negative and positive spins. It is shown by use of topological relations among these numbers that the magnetization of an Ising spin antiferromagnet increases stepwise at absolute zero with increasing field strength. The spin arrangement at each step is determined of Oguchi and Takano's model of CoC12 ·2H20 and the simple, body­ centered, face-centered cubic and MnF2 type lattices with nearest and next-nearest neighbor interactions. Experimental results of CoC12 • 2H20 are discussed as well.

A Statistical Model for the Dilute Ferromagnet

Abstract: A statistical model for a kind of dilute ferromagnetism is presented. In this model, a sublattice is a mixture of magnetic ions and non-magnetic ions, and the other sublattice is occupied exclusively by magnetic ions. Assuming the Ising type exchange interaction between magnetic ions, some exact results for the system are obtained. The Curie temperature decreases as the concentration of magnetic ions decreases and reaches the absolute zero of temperature at a critical concentration. At concentrations higher than the critical value, the specific heat remains finite and has a cusp with vertical tangent at the Curie temperature. The critical concentrations for several types of lattices are also given.

Relativistic Formulation of the Green's Function Method in Periodic Lattices

Abstract: A relativistic formulation of the Kohn-Rostoker Green's function method is developed in the Dirac formalism. The result is very simple. The matrix elements of the secular equa­ tion have the same form as the nonrelativistic matrix elements, and the relativistic structure constant consists of the summation of the products of a nonrelativistic structure constant and a Clebsch-Gordan coefficient over spin ± 1/2. Hence, a calculation of the relativistic matrix elements can be performed as easily as the nonrelativistic calculation, and the only problem is a significant increase in computing time which results from the doubling of the dimensions of the secular equation and the complex property of the matrix elements. The present paper also contains a brief discussion of the relativistic formulation of the APW method, and an expression for the matrix element corresponding to the nonrelativistic matrix element is proposed.

Simple Self-Consistent Treatment of Kondo's Effect in Dilute Alloys

Abstract: The self-consistent treatment of Kondo's effect by Nagaoka is revised by using the method of Gor'kov in the theory of superconductivity. Expressing the spin operators in terms of Fermi operators, such as Sz= (at+at-a.J.+a.t.)/2, the Green's functions of the type {ck'tSziCkt~ are decomposed into the sum of terms like

Corepresentations of Magnetic Point Groups

Abstract: The well-established theory due to Wigner of the corepresentations of non-unitary groups is here applied to the magnetic point groups and the results are tabulated. The equivalence of the theory of the corepresentations of the grey groups to the conventional treatment of time-reversal symmetry in space groups is also considered.

Short-Range Order for the Triangular and Honeycomb Ising Nets in Ferro- and Antiferromagnetic Cases

Abstract: The short-range order parameters are evaluated for the triang~lar and honeycomb Ising nets in ferro- and antiferromagnetic cases by the method of Kaufman and Onsager.l) For the antiferromagnetic triangular net we also evaluate the probabilities for the various spin configurations. When the three spins are located at the vertices of the smallest regular triangle, the probability that three neighbouring spins are all parallel is zero at T=O. However, it is 0.035120 or 0.202998 respectively at T=O according as the vertical angle of the three neighbouring spins is 120° or 180°. Making use of these values, the configurational probabilities corresponding to four or five neighbouring spins are also evaluated at zero temperature.

Ising Spin Models of Complex Ferrimagnetism

Abstract: A simple statistical model of ferrimagnetism is investigated based upon the results of the theory of crystal statistics. It is generally composed of three kinds of Ising spins, of which one forms a plane square lattice and the other two occupy the midpoints of each of the bonds in this plane square lattice. The complete spin arrangement makes up a decorated plane square lattice, in which there exists an antiferromagnetic exchange coupling between every pair of nearest neighbouring spins. Syozi and Nakano investigated ten years ago similar kinds of Ising spin models, which were, however, simpler than the present model. The temperature dependence of the spontaneous magnetization of such a ferrimagnetic Ising model is investi­ gated using the Onsager-Yang theory of crystal statistics. In addition to the features found by Syozi and Nakano, there appear some other features of this dependence which are not seen in the case investigated by them. The probability that two nearest neighbouring points of the lattice which consists of every midpoint are occupied by a pair of similar atoms and of dissimilar atoms is also investigated.