Sumiyoshi Fujiki

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

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 Kirkpatricks result is generalized and rederived without use of the replica method. For the short ranged model, i.e. a binary mixture of JA = -JB, the integral equation is solved exactly and the energy of the spin glass state is obtained at T = 0.

Possibility of the Kosterlitz-Thouless Phase Transition in the Two Dimensional Fully Frustrated Ising Model

Fully frustrated Ising models on two-dimensional lattice with the first and second or third nearest neighbor interactions are studied. Original Ising spin variables are transformed into the cell spin variables, whose Hamiltonian is derived. The interaction of states and the role of excited states are discussed. Order parameters of the fully frustrated systems are proposed in a unified way. Vortex and antivortex excitations are observed by Monte Carlo simulation. Results strongly predict the Kosterlitz-Thouless phase transition in the model.

Distribution of spins and the thermodynamic properties in the glass-like (spin glass) phase of random Ising bond models

The distribution of spins and the thermodynamic properties of random Ising bond models are obtained by the use of the integral equation for the distribution function of the effective fields g(l). The integral equation is derived for a general case in a simple way by the use of the Bethe approximation. From the relation between the magnetisation and the effective field, the phase boundaries between the paramagnetic phase, the glass-like (spin glass) phase (GLP) and the ferromagnetic phase are obtained for the general distribution P(J). For a binary mixture with JA=-JB, z=3, the integral equation is solved by approximating g(l) by a superposition of the delta functions. The specific heat and the susceptibility have cusps at the temperature TG, below which the glass-like phase appears.

Frustration effect on the d-dimensional Ising spin glass. I. Spin glass and dilution problems

The d-dimensional random bond Ising system is treated by the square approximation generalised for a random system. The expression of the uniform, staggered, and spin glass susceptibilities is obtained for the general distribution of the exchange interaction. The present approximation includes the closed-loop and frustration effects directly, the pure limit of which agrees with Kikuchis second approximation. A simple version of the above approximation is applied to the spin glass and dilution problem and the authors obtain the phase diagram of the ferromagnetic, spin glass and paramagnetic phases including the frustration effect.

XY-Nature of the Fully Frustrated Ising Model on the Triangular Lattice

The XY-nature of the Ising model on the triangular lattice with the antiferromagnetic nn and ferromagnetic nnn interactions is studied by Monte Carlo simulations. The order parameter is defined via the cell spin which represents a set of Ising variables in each frustrated unit cell. The finite size effects on the x y - and z -components of the order parameter are analyzed separately. The fluctuation of the absolute value of the order parameters is introduced as a generalized susceptibility. The successive phase transition feature with the Kosterlitz-Thouless-like phase is strongly confirmed. A non-universal character of the model is discussed.

Spin-glass phase in the site Ising model

For a random mixture of A and B spins in the site Ising model, with exchange energies JAA, JBB and JAB and the concentrations pA and pB, it is shown that it is possible for a spin-glass phase to exist for certain combinations of exchange energies and concentrations. The critical temperatures for paramagnetic-ferromagnetic, paramagnetic-antiferromagnetic and paramagnetic-spin-glass transitions, and the uniform, staggered, and spin-glass susceptibilities are obtained in the Bethe approximation. The Luttinger and Mattis models are also discussed.

Application of the Cluster Variation Method to the Ferromagnetic Six-State Clock Model on the Triangular Lattice and Its CAM Analysis

The cluster variation method is applied to the ferromagnetic six-state clock model on the triangular lattice up to the hexagonal cluster approximation. The Kosterlitz-Thouless type phase transition of the model is studied by using the coherent anomaly method (CAM).

Cube cluster approximation for the spin glass in the simple cubic lattice

Abstract The spin glass in the random-bond Ising model on a simple cubic lattice is considered. A simple method to calculate the partial trace of the density matrices of a fairly large cluster by use of the REDUCE system is presented. The phase diagram showing the paramagnetic, ferromagnetic, antiferromagnetic and spin glass states is obtained for the ± J model on the simple cubic lattice by the cube cluster approximation. The spin glass transition temperature is obtained with the inclusion of enough frustration of the cube clusters, and kT g/ J =0.9850 for p (the concentration of the + J bond) = 1/2.

Frustration effect on the d-dimensional Ising spin glass. II. Existence of the spin glass phase

For pt.I see ibid., vol.13, p.4723 (1980). The uniform, staggered, and spin glass susceptibilities chi u, chi s and chi g are calculated explicitly for the random bond Ising models on d-dimensional (d=2, 3, 4 and 6) cubic lattices, in the case of the binary mixture of equal strength JA=-JB, by the square approximation developed by Katsura and Fujiki (1980). This approximation includes directly the closed-loop and frustration effects, and the authors obtain the ferromagnetic, antiferromagnetic and spin glass transition temperatures Tc, TN and Tg. The values of both Tc and Tg are lower than those in the Bethe approximation. In dimensions d>or=4, slight decreases in Tg are obtained. The decreases in Tg are not small for d=2 and 3, but no drastic changes are observed. The spin glass states seem to be realised for d>or=2 at least as metastable states.

Fluctuation effect and the spin-glass transition temperatures in the random-bond Ising models in the hexagonal, triangular, BCC and other lattices-unified description

The cluster variational free energies of the random-bond Ising model are given in terms of effective fields and of effective interactions. The stationarity of the free energy gives the reducibilities between the one-body, two-body and cluster density matrices. From these reducibilities the uniform, staggered and spin-glass susceptibilities are obtained. A simple version of the above treatment is also presented which is called the cactus approximation. The phase diagrams of the binary (and ternary) mixtures of the ferromagnetic, antiferromagnetic (and non-magnetic) bonds in the triangular, hexagonal, and BCC lattices are obtained. The phase diagram of the triangular lattice is qualitatively similar to the FCC lattice and those of the hexagonal and BCC lattice to the square lattice. In particular the bond-diluted antiferromagnet in the triangular lattice is shown to have a spin-glass state.