Sakari Inawashiro

Mixture of Two Anisotropic Antiferromagnets with Different Easy Axes

Thermal and magnetic properties of a mixture of two anisotropic antiferro-magnets with different easy axes have been analyzed both in mean field approximation and in the method of distribution function. A new phase called OAF phase is found within a certain range of concentration. In OAF phase, the spin of each species of ion on a sublattice has each own axis of sublattice magnetization tilting oblique to the easy axes of the pure systems. As temperature increases, OAF phase makes a transition into the antiferromagnetic phase and then to the paramagnetic phase successively. It is expected that these transitions are detected by measurements of specific heats for a powder sample and of susceptibilities for a single crystal. It is also pointed out that magnetization processes show some characteristic features of OAF phase.

Lattice Green's Function. Introduction

Physical, analytical, and numerical properties of the lattice Greens functions for the various lattices are described. Various methods of evaluating the Greens functions, which will be developed in the subsequent papers, are mentioned.

Lattice Green's Functions for the Rectangular and the Square Lattices at Arbitrary Points

The lattice Greens functions of the rectangular and the square lattices Irect(a;m,n;α,β)≡1π2[double integral operator]0πcosmxcosny dx dya−ie−αcosx−βcosy,Isq(a;m,n)≡Irect(a;m,n;1,1) are considered. The integral Irect(a, m, n; α, β) for a > α + β is evaluated and expressed in terms of the generalized hypergeometric function F4. Expressions of Isq(a; m, n) for a > 2, a < 2, and a ∼ 2, and Irect(a; m, m; α, β) in terms of pFp−1 are presented by the method of the analytic continuation using the Mellin‐Barnes type integral. They are useful for the understanding of the nature of the singularity and for numerical calculation. The behaviors of Isq(a; m, n) are shown in figures.

Spin glasses for the infinitely long ranged bond Ising model and for the short ranged binary bond Ising model without use of the replica method

The long ranged Gaussian random Ising bond model and short ranged binary random Ising bond model are discussed by the method of the pair approximation of the cluster variation and by the method of the integral equation for the distribution function of the effective fields. For the long ranged model, Sherrington and Kirkpatricks result is generalized and rederived without use of the replica method. For the short ranged model, i.e. a binary mixture of JA = -JB, the integral equation is solved exactly and the energy of the spin glass state is obtained at T = 0.

Magnetic Properties of Solid Solution CoxFe1-xCl22H2O

The magnetic properties and the phase diagram of the solid solution Co x Ni 1- x Cl 2 6H 2 O are analyzed by using a model Hamiltonian with the mean field approximation. Our results are qualitatively in agreement with experimental ones. It is shown that the sublattice magnetization lies in a plane including both easy axes of two pure substances ( ca -plane) and its direction varies smoothly over the whole range of the concentration x , not within a limited range of x as observed in K 2 Mn x Fe 1- x F 4 and Co x Fe 1- x Cl 2 2H 2 O. The feature is due to off diagonal terms in the Hamiltonian which come from the non-orthogonality of the easy axes of two pure substances CoCl 2 6H 2 O and NiCl 2 6H 2 O (∼65°). The characteristic features of the magnetization processes are also analyzed considering the fact that the second easy axis of CoCl 2 6H 2 O does not lie within the ca -plane.

Nature of the Ordered Phase in a Hexagonal Ising Antiferromagnet

A Monte Carlo study of a hexagonal Ising Antiferromagnet reveals the occurrence of a new type of modulated phase in which a spin structure described by using three sublattices is randomly modulated in the lattice. The order parameter of this phase is not individual sublattice magnetizations but a symmetric function of them which corresponds to the magnetic structure factor F (1/3, 1/3, 0). As the temperature is decreased, this phase gradually changes into a usual homogeneous ferrimagnetic phase. This process is discussed in detail. It is suggested that this modulated phase occurs in CsCoCl 3 and CsCoBr 3 .

Linear Heisenberg Model of Ferro‐ and Antiferromagnetism

The partition function of the one‐dimensional Heisenberg model is considered. Hamiltonian of the system H=−12 ∑ [J⊥(σlxσl+1x+σlyσl+1y)+J∥σlzσl+1z]−mH ∑ σlz is expressed in terms of Fermi operators. The term which contains J∥, the quartic term and a part of quadratic term in Fermi operators, have been regarded as perturbation, keeping the symmetry with respect to the magnetic field. Linked‐cluster expansion in an appropriate form for this case has been developed and the partition function has been obtained up to the third order in J∥. Numerical values of energy, specific heat, and susceptibility up to second order in J∥ are shown. The ground‐state energy is EN|J⊥|=−2π−2π2(J∥|J⊥|)−16π3(16−π2144)(J∥J⊥)2+O[(J∥J⊥)3].E/N |J∥| for the antiferromagnetic case J∥ = −|J∥| = J is −0.8899. Agreement with the exact value, −0.8863, is quite satisfactory.

Competing Ising interactions and chaotic glass-like behaviour on a Cayley tree☆

For the Ising model on a Cayley tree with competing nearest neighbour coupling J and next nearest neighbour coupling J′, we find in addition to the expected paramagnetic, ferromagnetic and antiferromagnetic phases, an intermediate range of J′/J < 0 values where the local magnetization has chaotic oscillatory glass-like behaviour.

The energy of the spin-glass state of a binary mixture at T = 0 and its variational properties

In the random-bond model of Ising spins, the concept of a multiple-bond distribution of effective field was introduced in the pair approximation. The integral equation for a single-bond distribution was derived intuitively. The variational energy at T = 0 is expressed in terms of two parameters μ and η where μ is the probability of zero effective field in the single-bond distribution and η is the magnetization per spin. For η = 0, the energy of the spin-glass state corresponds to a local minimum as a function of μ, for an even z (number of the nearest neighbours) and to an inflection point for an odd z. It was shown that the spin-glass state corresponds to a local minimum with respect to μ and η for z = 4, to an inflection point with respect to μ and a local minimum with respect to η for z = 3. It is conjectured that the maximum of the energy of the spin-glass state of Sherrington and Kirkpatrick is attributed not to the replica method, but to the mean field approximation. Stationary properties of the energy as a function of both μ and η were examined in detail.

Lattice Green's function for the simple cubic lattice in terms of a Mellin‐Barnes type integral. II

The series representation of the lattice Greens function for the simple cubic lattice I(a)=π−3∫oπ∫oπ∫oπD−1dxdydz, where D=a‐ie‐cosx‐cosy‐cosz, around the singularity a=1 is obtained in fractional powers of a2−1 (convergent for |a2−1|<1), by the method of analytic continuation using a Mellin‐Barnes type integral and also by use of the analytic continuation of 3F2 (, , ; , ; 1) as a function of the parameter. It gives leading and full expansions near the singularity a=1.