Ikuo Ono

Theory of Critical Magnetic Scattering of Neutrons by Ferromagnet and Antiferromagnet

The statistical theory of the localized model of ferromagnetism has been developed using the effective Hamiltonian method. The present method is an extensive application of that by Strieb, Callen and Horwitz. The result is reduced to that of the Bethe approximation in the Ising model in one limit, and to that of the constant coupling approximation in the Heisenberg model in the other limit. The method has been generalized to calculate the spin pair correlation functions, which are very important for the cross section in the critical magnetic scattering of neutrons. The spin pair correlation functions have been obtained in Ornstein-Zernike type in the vicinity of the critical temperature. The results obtained by Elliott and Marshall, Mori and Kawasaki, and Tahir-Kheli and Callen are compared with the present results and are criticized. The present results are in good agreement with the experimental results. The method has been extended to the antiferromagnetic case.

Ground State and Phase Transition in the Quenched Random Mixture of Ferro-Antiferromagnets

The energy and spin pair-correlation in the ground state and the phase transition for a random mixture of the ferro-antiferromagnets in a quenched Ising system have been investigated by a new idea based on a division of the lattice into elementary units. The effects of the loop proper to the each lattices have been explicity considered. It is demonstrated that the transition temperatures are intimately related to the ground-state energy. Monte Carlo simulations performed on the square lattice are also reported.

Padé Approximation to Ferromagnet with Anisotropic Exchange Interaction

The Heisenberg model, the Ising model and the x y model in ferromagnetism are treated within a unified scheme. The exchange interaction between nearest neighboring spins i and j is -( J /2)[ a σ i z σ j z + b (σ i x σ j x +σ i y σ j y )], where J is the exchange integral, σ i the Pauli spin operator of the i -th spin, and a and b are parameters varying from 0 to 1, respectively. The high temperature series for the susceptibilities of linear chain, simple quadratic and simple cubic lattices are calculated up to the seventh order of J / k T . Pade approximation is applied to find the Curie point and the power of the singularity of the susceptibility. In the case of a =1 the Curie point is almost constant in the region \(0{\leq}b{\lesssim}0.7\) for simple quadratic and \(0{\leq}b{\lesssim}0.8\) for simple cubic lattice, respectively, but the convergence of Pade approximation becomes worse as b approaching 1.

Interface Approach to Phase Transitions and Ordering by Monte Carlo Simulations and Its Applications to Three-Dimensional Antiferromagnetic Potts Models

We develop an interface approach to bulk phase transitions and ordered states by using Monte Garlo simulations, and apply it to antiferromagnetic q -state Potts models with q =3∼6 on the simple cubic lattice. A stiffness exponent a defined by Δ F ∼ L a , where Δ F is the interface free energy for a system of size L , is introduced as a measure of the stiffness of the ordered phase against an external stress. Applying finite-size scaling to Δ F and to the squared order parameter enable one to determine each of T c , ν, β and γ in order where T c is the critical temperature and the others are critical exponents. This approach also provides a means to study properties of the ordered state through a and interface profiles. In the q =3 and 4 models the estimated exponents ν, β, γ and a indicate new universality classes. The q =5 model shows a phase transition, while the q =6 model does not. The q =3∼5 models have non-integer values of a at low temperatures. The phase transitions in these models are confirmed t...

Two-Magnon Bound States in a Linear Heisenberg Chain with Nearest and Next Nearest Neighbor Interactions

The bound state problems associated with two magnons in a linear chain of spin 1/2 with nearest and next nearest neighbor exchange integrals, J and α J , respectively, are studied. The Hamiltonian is rewritten in terms of the Fermi operators in place of spin operators, and an integral equation to determine the bound state energies is obtained. In the cases when the total wave number K of two magnons is π or π/2, analytical solutions are easily obtained. A part of the present results disagrees with Majumdars ones. Computer studies on the bound states are performed for a finite chain composed of spins up to twenty. They are consistent with the analytical results.

Occurrence of Kosterlitz-Thouless-Like Phase Transition in Antiferromagnetic Potts Models

Monte Carlo simulations of three-state Potts models interacting with nearest-neighbor antiferromagnetic J 1 ( 0) are carried out on a square lattice. At enough low temperatures an antiferromagnetic ordering is shown to appear except for J 2 =0. In the intermediate temperatures the occurrence of the Kosterlitz-Thouless-like phase is indicated from the estimation of the critical exponent η.

Phase Transitions in Quenched Random Mixtures on a Cactus Tree

A phase transition in a quenched ferro- and antiferromagnetic Ising mixture on an infinite triangular Cactus tree is rigorously studied. The non-periodic ordered phase which is specified by the “phase indicator” is determined so as to exhibit the highest transition temperature. This phase is intimately associated with the ground-state spin arrangement. The critical concentration below which the magnetization should disappear at the absolute zero is also derived.

Theory of a Disordered Heisenberg Model by the Coherent Potential Approximation

The averaged magnon Green function in a random Heisenberg ferromagnet which has two kinds of exchange integrals J A and J B randomly distributed is calculated by the coherent potential approximation. The density of states of magnon is calculated for various cases, and the correct localized mode is obtained in the low concentration limit. The critical concentration is obtained for two cases, J A >0, J B 0, J B =0. The magnetic properties for the two cases at the critical concentration are different from each other.

Statistical Theory of Bond-Random Ising Model on a Triangular Cactus Tree

Phase transitions of Ising model on a tree-like lattice having looped interactions are theoretically investigated. Concentration dependences of transition temperatures to a ferromagnetic ordered phase are rigorously obtained for several binary random-bond mixtures. For dilute ferromagnets magnetization, energies, spin-pair correlations, specific heats and susceptibilities have been evaluated in the ordered phase as well as in the paramagnetic phase. Spatial distributions of local magnetizations are estimated.

Analytical Methods and Computer Calculations of XY Model with Impurity Spin

The one dimensional XY model of spin 1/2 is discussed by transforming the spin operators to the Fermi operators. This method can be applied to the XY model with an impurity spin. In that case a pair of localized exciton (or a kind of magnon) levels are obtained. The energy of states can be determined by distributing the excitons over two sets of exciton levels which depend on whether the number of excitons is even or odd. The energy levels of states are calculated by the computer for small rings of 4, 6 and 8 spins. The results can be perfectly understood by the theory.