T. Kaneyoshi

A review is given of the differential operator technique in the Ising spin systems. The theoretical frameworks of the various models are discussed on the basis of the Ising spin identities. These can be applied to examine the magnetic properties in a variety of magnetic materials.

Abstract Magnetic properties (phase diagram and magnetization) of a cylindrical Ising nanowire or nanotube are investigated by the use of the effective‐field theory with correlations. Particular emphasis is given to the effects of the surface and its dilution on them. Much attention is paid to the thermal variation of the magnetization when the spins at the surface are coupled antiferromagnetically to the ferromagnetic core spins by the negative shell coupling. The effects of dilution at the sur

A new method incorporating the effects of many-body static spin correlations into an effective-field theory is discussed. The method is based on the introduction of a differential operator and the concept of the correlated effective field into two exact Callen identities of the Ising model. The resulting statistical theory is shown to have an accuracy equivalent to that of the Bethe-Peierls method. It is shown that the correlated-effective-field parameter at the transition temperature has a univ

A semi-infinite ferromagnetic simple cubic Ising lattice which has nonmagnetic impurities substituted for the magnetic species only at the surface is investigated with the use of a new type of effective-field theory with correlation. The surface magnetism is examined as a function of modified exchange ${J}_{s}=J(1+\ensuremath{\Delta})$ and concentration $P$ of magnetic atoms at the surface. The critical value ${\ensuremath{\Delta}}_{c}$, transition temperatures ${T}_{c}^{s}$, and phase diagram f

The critical behavior of a mixed ferromagnetic Ising spin system consisting of spin\(-\tfrac{1}{2}\) and spin-1 with a crystal-field interaction is investigated by the use of the effective-field theory with correlations. The general expressions for evaluating the Curie temperature and the tricritical point are obtained. We find that the tricritical point exists in the system with Z >3, where Z is the coordination number.

The magnetic properties of a diluted spin-2 and spin-5/2 ferrimagnetic Ising system are investigated on the basis of the effective-field theory with correlations. In particular, the effect of a positive single-ion anisotropy D on the compensation temperature in a pure system with D only on spin-5/2 atoms is investigated, in order to clarify the characteristic feature of the temperature dependence of the total magnetization M observed in a molecular-based magnetic material, . The influences of D

An effective-field theory that has recently been used for studying higher-spin Ising models is herein extended to the transverse Ising model with an arbitrary spin S. The general formulation for evaluating the transition line in the \ensuremath{\Omega}-T space and relevant statistical-mechanical quantities is derived. Numerical results are performed and analyzed for the particular cases S=3/2 and S=2.

A review is given of surface magnetism. In particular the interplay of magnetization and anisotropy at a surface is discussed, after a survey of experimental and theoretical results for magnetic moment and anisotropy at surfaces or interfaces of semi-infinite magnets and thin films. Finally, the importance for surface (or interface) analysis of the random single-ion anisotropy model is stressed.

Abstract The phase diagrams of a ferroelectric small particle described by the transverse Ising model (TIM) are investigated by the use of two theoretical frameworks, namely the standard mean‐field theory and the effective‐field theory corresponding to the Zernike approximation. The particle is represented by a two‐dimensional array of pseudo‐spins with two types of exchange interactions ( J in bulk and J S on the surface) and two types of transverse fields ( Ω in the bulk and Ω S on the surface