Itiro Syozi

A Statistical Model for the Dilute Ferromagnet

A statistical model for a kind of dilute ferromagnetism is presented. In this model, a sublattice is a mixture of magnetic ions and non-magnetic ions, and the other sublattice is occupied exclusively by magnetic ions. Assuming the Ising type exchange interaction between magnetic ions, some exact results for the system are obtained. The Curie temperature decreases as the concentration of magnetic ions decreases and reaches the absolute zero of temperature at a critical concentration. At concentrations higher than the critical value, the specific heat remains finite and has a cusp with vertical tangent at the Curie temperature. The critical concentrations for several types of lattices are also given.

Symmetrical Properties of Two-Dimensional Ising Lattices

Some symmetrical properties on the statistics of two-dimensional Ising lattices are studied. It is shown that such considerations give us very useful suggestions even for cases in which we know no exact solution. We investigate especially the cases of the square, triangular, honeycomb and generalized square lattices, with respect to the expressions of spontaneous magnetizations and susceptibilities.

Dualities for Extended Potts Models Induced from the Percolation Problems of Block Elements

The Potts model is extended to include the case of block type many-body interaction. The dilute ferromagnet on the block lattice is discussed as an extended Potts model with layers of lattice by using the real replica method. As a new type of self-dual lattice, the overlap-block lattice consisting of a block lattice and its dual lattice, is shown to have a Potts model structure. The dualities for those extended Potts models are proved on the basis of equivalences of the models to the percolation problems.

Potts Model of Magnetic Mixture in Annealed System

The properties of the random bond {f-state Potts models with the ferromagnetic and the antiferromagnetic interactions are investigated in the annealed system on two-dimensional decorated lattices. The ferromagnetic phase exists for all values of q and the intermediate phase appears between the ferromagnetic and the paramagnetic phases for {f > 4. On the other hand, the antiferromagnetic phase exists for only the value of {f < {fe, where {fc is the critical value of (f at which the antiferromagnetism of the antiferromagnetic Potts model with the uniform bond strength disappears. Especially for the decorated triangular lattice, the phase diagrams are investigated in details.