Yohtaro Ueno

Random Ordered Phase Characteristic of Quenched Mixtures of Ising Spins

A new ordered phase, tentatively called “random ordered phase” (ROP) is proposed in the quenched Ising spin system in which ferro- and antiferromagnetic exchange integrals exist. In the ROP each spin points to the same direction as the molecular field which is either up or down and is altered from site to site according as the various situations of surroundings. The phase transition is characterized by “random magnetization” and “random susceptibility”, whose expressions are given.

Interfacial approach tod-dimensional ±J Ising models in the neighborhood of the ferromagnetic phase boundary

Two- and three-dimensional ±J Ising models in the neighborhood of the ferromagnetic phase (FP) boundary in the concentration-temperature (p-T) plane are studied, investigating the size dependence of interfacial free energies calculated by a transfer matrix method. Thep andT dependences of two stiffness exponents relevant to the FP and the nonferromagnetic ordered phase lead to the following results in two dimensions, giving a unified view. It is confirmed that the random antiphase state (RAS) exists in contact with the vertical FP boundary. Spatial fluctuations are dominant near the vertical boundary, which is separated by the Nishimori line from the remaining FP boundary governed by thermal fluctuations. The RAS is a kind of Mattis spin glass such that it changes to the FP smoothly with nonsingular physical connectivity, but with a percolation singularity of its ferromagnetic part. Universal finite-size critical amplitudes are consistent with them. Results in three dimensions give only suggestions which are similar to the two-dimensional results. These results suggest important insight into spin-glass properties in higher dimensions.

Interface Approach to Phase Transitions and Ordering by Monte Carlo Simulations and Its Applications to Three-Dimensional Antiferromagnetic Potts Models

We develop an interface approach to bulk phase transitions and ordered states by using Monte Garlo simulations, and apply it to antiferromagnetic q -state Potts models with q =3∼6 on the simple cubic lattice. A stiffness exponent a defined by Δ F ∼ L a , where Δ F is the interface free energy for a system of size L , is introduced as a measure of the stiffness of the ordered phase against an external stress. Applying finite-size scaling to Δ F and to the squared order parameter enable one to determine each of T c , ν, β and γ in order where T c is the critical temperature and the others are critical exponents. This approach also provides a means to study properties of the ordered state through a and interface profiles. In the q =3 and 4 models the estimated exponents ν, β, γ and a indicate new universality classes. The q =5 model shows a phase transition, while the q =6 model does not. The q =3∼5 models have non-integer values of a at low temperatures. The phase transitions in these models are confirmed t...

Statistical Theory of the Random Ordered Phase in Quenched Bond Mixtures

Statistical theory based on generalized Bethe approximation is developed for the Ising quenched bond model in which ferromagnetic and antiferromagnetic exchange integrals exist. The random ordered phase (ROP) proposed in a previous paper is obtained. The random susceptibility χ r is calculated, and it is found that χ r diverges at the critical temperature T c . It is pointed out that the ordinary susceptibility for the uniform field might have a cusp at T c .

Statistical Theory of the Random Ordered Phase in the Bond Model: Uniform Magnetization

A statistical theory of the random ordered phase, proposed by Ueno and Oguchi, in the quenched random mixture with differentsigned exchange interactions is developed further, based on the generalized Bethe approximation. Specially the uniform magnetization in ferro-rich side and the sublattice magnetization in antiferro-rich side are obtained, which cannot be calculated in previous papers.

Suppressed Frustration Models and Related Models in Two Dimensions

Three kinds of models with finite ground states are studied: a) A triangular Ising frustration model in which frustration is suppressed by nnn interactions, b) a triangular XY frustration model in which discrete degeneracy occurs, and c) an antiferromagnetic 3-state Potts model on a square lattice in which degeneracy is reduced by nnn interations. A description by block spins via a continuous spin transformation reduces them to a generalized 6-state clock model with cos (θ i -θ j ) and cos 3(θ i -θ j ) forms of interactions for a) and to a coupled system of Ising and XY spins for b). Model c) becomes similar to model a). Simple analyses of these equivalent models give the critical temperatures of both transitions into a Kosterlitz-Thouless phase and a longe range order, which are quite consistent with those by computer experiments. Simplified models for a) and c) are also studied and an anisotropic case is considered for a).

Phenomenological Theory of the Random Ordered Phase

Very recently Miyako et aJ.ll ,2l have observed nonlinear susceptiblities in some dilute magnetic alloys. They (X 2 and X4) seem to show a divergent behavior at the freezing temperature Tr. The divergence of X2 at Tr was predicted first by Katsura3 l and phenomenologically by SuzukiY Takayama5l also obtained this result on the basis of the ROP.6 l, 7 l Ueno8l showed exactly the divergence of X2 in the spherical model with random infinite-ranged interactions. For the experiments by Miyako et al., 1, 2J Suzuki9 l gave a comment by presenting a phenomenological theory of the ROP. His theory does not seem to be compatible with the original idea of the ROP nor the experiment. We shall show another one and try to interpret the experiments, in particular, that on (Ti 1 -x V x) 2 03. 2) As Toulouse pointed out, 10 l the frustration effect plays an essential role in the competing random bond system. It is necessary for the frustration to occur that the lattice has closed loops. Works based on the ROP took account of the frustration effect by investigating clusters with closed loops.7l ,lu Takayama5l treated this effect by using a phenomenological parameter. On the other hand, in many of the theories in which the Edward-Anderson order parameter was used, it is not clear how the frustration is taken into account. The replica method of spin glass 12l seems to obscure it. It is also difficult to trace the effect in the theory of the GLP.13l, 3l Recently, making use of the gauge invariance and the measure of frustration introduced by Toulouse, several authors studied the ground-state properties14 l and made a reformation in terms of the frustration.\5)

Statistical Theory of the Random Ordered Phase in a Bethe Lattice

The random ordered phase (ROP) proposed in a previous paper by us is investigated in a Bethe lattice. The critical temperature T c , the random susceptibility χ r and the uniform susceptibility χ u are obtained rigorously by use of the effective Hamiltonian method. χ r diverges at T c , while χ u makes a cusp at T c . The spin glass phase in the Bethe lattice is discussed. It is concluded that the phase transition takes place between paramagnetic phase and ROP, and neither ferromagnetic nor spin glass phase can exist in the Bethe lattice.

Ordering and Phase Transitions Due to Entropy Gains in Two-Dimensional Frustration Models

Layered and isotropic frustration models on a square lattice are studied in a systematic way from the viewpoint of seeing how frustrations affect ordering. Ordering is attributed to entropy gains, which is analysed introducing cluster (C) regions and entropy-yielding (S) regions. These local structures are closely related to excited states with the lowest energy, which is investigated through the configurations of unsatisfied bonds (or strings). Searching for the conditions for local coupling between C regions via a S region and then for global ordering we reach the same results on the ordering for the layered models as those obtained by Hoever et al. For some isotropic models as well as layered ones the temperature dependence of interface tension is calculated. The former models show re-entrant phenomena characteristic of this type of phase transitions. The symmetry of frustration configuration and its breaking are also discussed.

Statistical Theory of the Random Ordered Phase in the Site Model

A statistical theory of the random ordered phase, proposed by Ueno and Oguchi, is discussed in the quenched random site model with two kinds of atoms, which is ferromagnetic or antiferromagnetic in the pure limits, respectively. The theory would be applicable to the mixed K 2 Cu x Fe 1- x F 4 .