Ojiro Nagai

Structure of Ground States of Antiferromagnetic Ising Model with General-Spin on Triangular Lattice

We investigate theoretically the structure of the ground states of the antiferromagnetic Ising model of general-spin S on the triangular lattice. It is shown that a three-sublattice structure is stable as the ground state of the Ising model of infinite-spin. A phenomenological discussion is given for the structure of the ground states for the Ising model of finite-spin.

A Short Range Order Effect in Antiferromagnetics

A statistical theory of antiferromagnetism, which is an extension of Nakamuras and Kasteleijn and Kranendonks theory, is developed. Our theory reasonably well explains the unusual behaviors of paramagnetic susceptibilities of CuF 2 ·2H 2 O and CuCl 2 ·2H 2 O. The theory is compared with experiments, and the following information is obtained. In the case of CuF 2 ·2H 2 O, the ferromagnetic exchange coupling constant is smaller than about 1/3 of the antiferromagnetic exchange coupling constant. The ratio of these two exchange coupling constants in CuCl 2 ·2H 2 O is about 0.55, which differs from 0.3 proposed by Oguchi and 0.165 by Marshall.

Low- and High-Temperature Behaviors of Ferromagnetic Ising Model of Infinite-Spin

We investigate low- and high-temperature properties of the ferromagnetic Ising model of infinite-spin. By using the cummulant expansion methods, we obtain low-temperature expansions of the free energy, the specific heat, the spontaneous magnetization, the zero-field susceptibility and so on, and high-temperature expansions of the free energy and the zero-field susceptibility. We compare the results with those obtained by Thompson for the system on the one-dimensional lattice, with those by using Monte Carlo simulations for the systems on the square lattice and on the simple cubic lattice and with those with the aid of the mean-field approximation.

Surface Magnons and Surface Spin Arrangements in Heisenberg Magnets with Two Kinds of Exchange Interactions

Acoustic surface-magnon spectra are calculated for semi-infinite ferro- and antiferromagnets, where spins are coupled via exchange interactions both with nearest neighbors ( J 1 ) and with next-nearest neighbors ( J 2 ). It is found that, when the parameter α= J 2 | J 1 | lies in certain intervals, the surface-magnon frequency is negative or imaginary, although the bulk-magnon frequencies remain real and positive. This condition indicates that the uniform ferro- or antiferromagnetic spin arrangement is not stable. For several cases of this type, it is shown that nonuniform spin arrangement, characterized by a rearrangement of spins in the surface region, has a lower classical spin-ordering energy than the uniform state, and hence is stable. In various cases, various different arrangements of surface spins are found to be stable, including a helical arrangement, in which spins in the surface region are ordered with helical symmetry while bulk spins are in an antiferromagnetic state.

Spin-ordering of the antiferromagnetic Ising model with general spin S on a triangular lattice

Abstract We study the antiferromagnetic Ising model with spin S on a triangular lattice by the use of Monte Carlo simulations. If S is larger than 11/2, we find that a long-range order exists at zero temperature and a KT-type phase transition occurs at a finite temperature.

Low temperature phase of the antiferromagnetic Ising model on a stacked-triangular lattice

Abstract The spin structure in the low temperature phase of a stacked-antiferromagnetic-triangular Ising lattice is investigated by the use of Monte Carlo simulations. We conclude that the structure, ( M , − M 2 , − M 2 ), proposed by Blankschtein et al., is one of the solutions but may not be realized as a stable solution.

Spin structure of the antiferromagnetic continuous-spin Ising model on a stacked-triangular lattice

Abstract The spin structure of the antiferromagnetic continuous-spin ( S =∞) Ising model on a stacked-triangular lattice is investigated by the use of Monte Carlo simulations. We find that the spin structure is the ferrimagnetic structure ( M , − m , − m ) in the low temperature region and the partial-disorder structure ( M ′, 0, −- M ′) in the intermediate temperature region.

Low-Temperature Behaviors of Antiferromagnetic Ising Model of Infinite-Spin on Triangular Lattice

We investigate low-temperature behaviors for an antiferromagnetic Ising model of infinite-spin on the triangular lattice. The internal energy, the specific heat, and the spontaneous sublattice-magnetizations are calculated by Monte Carlo simulations at low temperatures. The low-temperature expansions of the internal energy and the specific heat are obtained from a low-temperature expansion of the free energy and show excellent agreements with the results by the Monte Carlo simulations. The zero-temperature value of the specific heat is found to be equal to 2/3. The effects of the misfits of the first order are discussed.

Monte Carlo studies for three-dimensional quantum-spin models

Abstract The Monte Carlo simulations (MCS) for a Heisenberg magnet are attempted, by following the Suzuki-Cullen-Landau scheme. The critical temperature found is 0.85 J / k B . Also, the MCS for the transverse-Ising model are implemented. The computed critical line is compared with that obtained by Elliott and Wood.

Spin-ordering property of Ising model with general spin S on an antiferromagnetic triangular lattice

Abstract We study the antiferromagnetic Ising model with spin S on a triangular lattice by the use of Monte Carlo simulations. If S is larger than 11 2 , we find that a long range order exists at zero temperature and a “phase transition” occurs at a finite temperature.