Shigetoshi Katsura

Bio: Shigetoshi Katsura 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 24, co-authored 84 publications receiving 1812 citations. Previous affiliations of Shigetoshi Katsura include Tokyo Denki University.

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.

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.

One‐Dimensional Ising Model with General Spin

Abstract: The one‐dimensional Ising model with general spin S has been formulated as an eigenvalue problem of order 2S + 1. Two methods to reduce the order to [S + 1] have been developed for calculating the energy and the susceptibility at zero external field. Exact solutions for S = 32 and S = 1 have been obtained. Numerical calculations of S = 32, 1, and ½ have been compared.

Spin glasses: Experimental facts, theoretical concepts, and open questions

Abstract: This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

The theory of equilibrium critical phenomena

Abstract: The theory of critical phenomena in systems at equilibrium is reviewed at an introductory level with special emphasis on the values of the critical point exponents α, β, γ,..., and their interrelations. The experimental observations are surveyed and the analogies between different physical systems - fluids, magnets, superfluids, binary alloys, etc. - are developed phenomenologically. An exact theoretical basis for the analogies follows from the equivalence between classical and quantal `lattice gases' and the Ising and Heisenberg-Ising magnetic models. General rigorous inequalities for critical exponents at and below Tc are derived. The nature and validity of the `classical' (phenomenological and mean field) theories are discussed, their predictions being contrasted with the exact results for plane Ising models, which are summarized concisely. Pade approximant and ratio techniques applied to appropriate series expansions lead to precise critical-point estimates for the three-dimensional Heisenberg and Ising models (tables of data are presented). With this background a critique is presented of recent theoretical ideas: namely, the `droplet' picture of the critical point and the `homogeneity' and `scaling' hypotheses. These lead to a `law of corresponding states' near a critical point and to relations between the various exponents which suggest that perhaps only two or three exponents might be algebraically independent for any system.

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...