Sakari Inawashiro

Bio: Sakari Inawashiro is an academic researcher from Tohoku University. The author has contributed to research in topics: Ising model & Spin glass. The author has an hindex of 17, co-authored 54 publications receiving 941 citations. Previous affiliations of Sakari Inawashiro include University of Melbourne.

Lattice Green's Function. Introduction

Abstract: Physical, analytical, and numerical properties of the lattice Green's functions for the various lattices are described. Various methods of evaluating the Green's functions, which will be developed in the subsequent papers, are mentioned.

Mixture of Two Anisotropic Antiferromagnets with Different Easy Axes

Abstract: Thermal and magnetic properties of a mixture of two anisotropic antiferro-magnets with different easy axes have been analyzed both in mean field approximation and in the method of distribution function. A new phase called OAF phase is found within a certain range of concentration. In OAF phase, the spin of each species of ion on a sublattice has each own axis of sublattice magnetization tilting oblique to the easy axes of the pure systems. As temperature increases, OAF phase makes a transition into the antiferromagnetic phase and then to the paramagnetic phase successively. It is expected that these transitions are detected by measurements of specific heats for a powder sample and of susceptibilities for a single crystal. It is also pointed out that magnetization processes show some characteristic features of OAF phase.

Lattice Green's Functions for the Rectangular and the Square Lattices at Arbitrary Points

Abstract: The lattice Green's functions of the rectangular and the square lattices Irect(a;m,n;α,β)≡1π2[double integral operator]0πcosmxcosny dx dya−ie−αcosx−βcosy,Isq(a;m,n)≡Irect(a;m,n;1,1) are considered. The integral Irect(a, m, n; α, β) for a > α + β is evaluated and expressed in terms of the generalized hypergeometric function F4. Expressions of Isq(a; m, n) for a > 2, a < 2, and a ∼ 2, and Irect(a; m, m; α, β) in terms of pFp−1 are presented by the method of the analytic continuation using the Mellin‐Barnes type integral. They are useful for the understanding of the nature of the singularity and for numerical calculation. The behaviors of Isq(a; m, n) are shown in figures.

On the Acoustic Radiation from a Flanged Circular Pipe

Abstract: The problem of sound radiation from a circular pipe fitted with an infinite flange is solved. The radiation impedance, the transmission coefficient, the power gain function and the end correction are evaluated numerically and shown as functions of the wave length.

Spin glasses for the infinitely long ranged bond Ising model and for the short ranged binary bond Ising model without use of the replica method

Abstract: The long ranged Gaussian random Ising bond model and short ranged binary random Ising bond model are discussed by the method of the pair approximation of the cluster variation and by the method of the integral equation for the distribution function of the effective fields. For the long ranged model, Sherrington and Kirkpatrick's result is generalized and rederived without use of the replica method. For the short ranged model, i.e. a binary mixture of J A = - J B , the integral equation is solved exactly and the energy of the spin glass state is obtained at T = 0.

Experiments on simple magnetic model systems

Abstract: “…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will a...

Theory of monomer-dimer systems

Abstract: We investigate the general monomer-dimer partition function, P(x), which is a polynomial in the monomer activity, x, with coefficients depending on the dimer activities. Our main result is that P(x) has its zeros on the imaginary axis when the dimer activities are nonnegative. Therefore, no monomer-dimer system can have a phase transition as a function of monomer density except, possibly, when the monomer density is minimal (i.e. x = 0). Elaborating on this theme we prove the existence and analyticity of correlation functions (away from x = 0) in the thermodynamic limit. Among other things we obtain bounds on the compressibility and derive a new variable in which to make an expansion of the free energy that converges down to the minimal monomer density. We also relate the monomer-dimer problem to the Heisenberg and Ising models of a magnet and derive Christoffell-Darboux formulas for the monomer-dimer and Ising model partition functions. This casts the Ising model in a new light and provides an alternative proof of the Lee-Yang circle theorem. We also derive joint complex analyticity domains in the monomer and dimer activities. Our considerations are independent of geometry and hence are valid for any dimensionality.