Koh Wada

Monte Carlo Study of a Triangular Ising Lattice. II. Occurrence of the Kosterlitz-Thouless-Like Phase Transition

A two-dimensional triangular Ising lattice with the nearest-neighbor antiferromagnetic interaction J 1 and the next-nearest-neighbor ferromagnetic interaction - J 2 is studied by the Monte Carlo simulation. It is shown that the system with a finite J 2 undergoes the successive phase transition, paramagnetic→Kosterlitz-Thouless (KT)-like→ferrimagnetic phases, as temperature decreases. The sub-lattice switching phenomenon observed in our previous work is shown to be an intrinsic property inherent to the present system which has an XY character. The marginal exponent of the order-parameter correlation function at the KT-like transition point is seen to increase from 1/4 as the ratio J 2 / J 1 decreases, namely, it reveals a deviation from the universal behavior of a genuine XY model.

Reformulation of the path probability method and its application to crystal growth models

The microscopic master equation of a system is derived within the framework of the path probability method (PPM). Then, by extending Moritas method in equilibrium statistical mechanics, the path probability function constructed microscopically can be systematically decomposed to result in the conventional path probability function of cluster approximation when correlations larger than the chosen basic cluster are neglected. In order to critically compare the master equation method with the PPM, the triangle approximation is treated by both methods for crystal growth models. It is found that the PPM gives physically satisfactory kinetic equations, while the master equation (supplemented with a cluster probability in the superposition approximation) does not. The triangle PPM calculation considerably improves the result of the pair approximation for crystal growth velocity in the solid-on-solid model, and compares well with Monte Carlo results.

Monte Carlo Simulation of a Triangular Ising Lattice

The Monte Carlo simulation has been made on a triangular Ising lattice with antiferromagnetic nearest neighbor and ferromagnetic next nearest neighbor interactions. It is conjectured that a thermodynamically stable antiferromagnetic state does not exist in this model.

Monte Carlo Study of a Triangular Ising Lattice. I

Monte Carlo calculations have been used to study the spin ordering on a triangular Ising lattice with antiferromagnetic nearest neighbor and ferromagnetic next nearest neighbor couplings. It is suggested that a partially disordered antiferromagnetic phase does not occur stably because the sublattices interchange their roles among them due to lattice symmetry.

Coherent-Anomaly Method Calculation on the Cluster Variation Method.I

On the basis of the coherent-anomaly method (CAM) proposed by Suzuki, the static and dynamic critical exponents of the Ising model in the triangle and the square lattice are calculated using the cluster variation method (CVM) and the path probability method (PPM) devised by Kikuchi within analytical tractable approximations. The values of critical temperatures and critical exponents estimated from three approximations with different levels are generally reasonable. The two-dimensional results are also compared with those of the simple cubic lattice.

Microscopic kinetic mechanism in current-induced conversion on Si(001) vicinal surface

The microscopic mechanism of current-induced domain conversion phenomena on the Si(001) vicinal surface during annealing is studied using the kinetic equation derived by the path probability method (PPM) in irreversible statistical mechanics along with the Monte Carlo simulation. In addition to evaporation, our model takes account of the three effects related to migration of surface atoms: anisotropic migration on the Si(001) 2×1 reconstructed surface, the electromigration effect and asymmetry in step kinetics (Schwoebel effect) which takes the difference in the kinetics between two types of steps into account. The numerical calculation of the kinetic equation reproduces the domain conversion when the Schwoebel effect exists. The differences in the movements of two types of steps and the spreading velocities of major domains observed during domain conversion are also shown. The results suggest that the combination of the three migration effects causes the difference in the kinetics of atoms between two types of steps, which leads to the domain conversion. The results of the Monte Carlo simulation are in good agreement with those of the PPM.

The CAM Calculation of Critical Exponent ν by the Cluster Variation Method

The critical exponent ν of correlation length is calculated on the basis of the coherent anomaly method (CAM) by using the pair, the cactus-square and the square approximations of the cluster variation method (CVM) in the D (≥2)-dimensional cubic lattice of the Ising model. These simple analytical approximations give good values of critical exponent ν and critical temperature in the two- and three-dimensional lattices. However, further consideration is needed to determine a critical dimension in the D -dimensional Ising model by the CAM.

Application of the Cluster Variation Method to Spin Ice Systems on the Pyrochlore Lattice

The cactus approximation in the cluster variation method is applied to the spin ice system with nearest neighbor ferromagnetic coupling. The temperature dependences of the entropy and the specific ...

Dynamical Susceptibility in KH2PO4-type Crystals above and below Tc

The time dependent cluster approximation called the path probability method (PPM) is applied to a pseudo-spin Ising Hamiltonian of the Slater-Takagi model for KH 2 PO 4 -type hydrogen-bonded ferroelectrics in order to calculate the homogeneous dynamical susceptibility χ(ω) above and below the ferroelectric transition temperature T c . Above the transition temperature all the calculations are carried out analytically in the cactus approximation of the PPM. Below the transition temperature the dynamical susceptibility is also calculated accurately since the analytical solution of spontaneous polarization in the ferroelectric phase can be utilized. When the temperature is approached from both sides of the transition temperature, only one of relaxation times shows a critical slowing down and makes a main contribution to the dynamical susceptibility. The discrepancy from Slater model (ice-rule limit) is discussed in comparison with some experimental data.

Application of the cluster variation method to anisotropic polarization fluctuations in KD2PO4-Type crystals above and below the transition temperature

The cluster variation method (CVM) in the cactus approximation is applied to a pseudo-spin Ising Hamiltonian of the Slater-Takagi model for KD 2 PO 4 -type hydrogen-bonded ferroelectrics to calculate the wave-number dependent susceptibility χ( q ), mainly focussing on the ferroelectric phase. The strong anisotropy of polarization fluctuations along the easy z -axis is shown to appear not only in the paraelectric phase but also in the ferroelectric phase when the ice-rule limit is approached. An analytical expression of the spontaneous polarization is fully utilized for calculations on χ( q ) below the transition temperature.