Chikao Kawabata

Statistical Thermodynamics of Finite Ising Model. II

The partition functions of the two- and three-dimensional finite Ising models in the presence of a magnetic field have been calculated with use of a high-speed computer. Periodic boundary conditions were imposed. All the numbers of configurations for the 3×3×3, 5×5, and 4×6 lattices are tabulated. The distribution of zeros of the partition functions in the complex magnetic-field plane has been obtained both for the ferro- and antiferromagnetic cases. The zeros in the ferromagnetic cases are distributed on the unit circle according to the Yang-Lee theorem, and the dependence on temperature of the distribution functions has been studied. In the antiferromagnetic case most of zeros are on the negative real axis, but a certain number of complex roots appear in the left half of the plane. The magnetization and the magnetic susceptibility have been calculated as functions of temperature.

A linearlike Tc dependence vs spacing d between Cu-O (or other elements) sheets for C-axis in perovskite structure

Photographs of high T c copper-oxide Tl-, Bi-, Y-, Eu- and Nd-superconductors taken by a high-resolution transmission electron microscope were analyzed using an image processing computer. We found that the critical temperature T c follows a linearlike dependence versus spacing d between Cu-O (or other elements) sheets for the c -axis in a perovskite structure within a spacing range of 3∼4 A. Our empirical formula is consistent with many experimental results for copper-oxide high T c materials discovered so far. We predict that a universal line for T c vs d exists. We obtained critical spacing d c of superconducting phase transition. We also propose a method of creating new copper-oxide higher T c materials.

Monte Carlo simulations of the two-dimensional quantal and classical spin systems — A new type of phase transition with vortices☆

Abstract A new type of phase transition has been found in the two-dimensional XY-model using Monte Carlo simulations, which show a divergence of susceptibility, but no divergence of specific heat. Vortices appear below Tc as was predicted by Kosterlitz and Thouless.

Statistical mechanics of three - dimensional finite Ising model

Abstract The partition function of a three-dimensional Ising model was calculated by a high-speed computer for a cubic array of twenty-seven points. The zeros of the partition function and the specific heat were obtained.

Monte Carlo simulation of quenched two-dimensional single spin flip kinetic Ising model

Abstract Monte Carlo simulation was performed for finite two-dimensional single spin flip kinetic Ising model which is quenched from a thermodynamically stable to an unstable state. The magnetization, the structure function S(K, t) and its half width are obtained.

Statistical Mechanics of the Finite Ising Model with Higher Spin

The partition functions of the finite Ising models of spin S =1, 3/2, 2, 5/2 and 3 have been calculated by a high speed computer. The periodicity condition at the boundaries has been imposed, and only the nearest neighbor interaction has been assumed. The specific heats of these finite systems have been calculated as a function of temperature. The maxima of the specific heat increase proportionally to long N in the two-dimensional Ising model with spin S =1, N being the number of lattice points, which indicates that the specific heat for the above lattice has a singularity such as C v / k ∼ A log | T - T c |+ B ± : A ∼0.10 and B - - B + =0.24. The difference ( B + - B - ) has been estimated from the asymmetric distribution of the zeros of the partition function in the complex temperature plane.

Monte Carlo simulation of two-dimensional Ising model with logarithmic exchange interaction

Abstract Monte Carlo simulation was done to a 2-D Ising model with exchange interaction depending logarithmically on distance. This model is equivalent to a 2-D Coulomb gas. A configuration corresponding to bound pairs of opposite charges appears below Tc, while above Tc pairs are dissolved into free charges.

Simulation of the dynamic structure factor for two-dimensional classical Heisenberg ferromagnets

Abstract Using a combined Monte Carlo-molecular dynamics technique we have studied the dynamic structure factor S ( q , ω) on a square lattice for the isotropic Heisenberg and planar ferromagnetic Hamiltonians. Dynamical signatures of the Kosterlitz-Thouless transition in the planar case are suggested.

Statistical mechanics of the finite Heisenberg model

Abstract The eigenvalues of the finite Heisenberg model such as the 3 × 3 and 2 × 2 × 2 lattices ( s = 1 2 ) were obtained. The zeros of these partition functions are investigated numerically in the complex temperature plane.

An Application of Padé Approximants to Heisenberg Ferromagnetism and Pair-Product Model

The method of Pade approximants is applied to the high-temperature series for the susceptibility of the Heisenberg and pair-product models. It is concluded that in both cases the susceptibilities diverge as χ 0 ∝|T-T c | -γ , where γ is nearly \(\frac{4}{3}\) in three dimensions.