Magnetic properties and distribution of thermal averages of spins in the one-dimensional random mixture of Ising spins of S = 1 and12

The one-dimensional magnetic mixture of two kinds of magnetic ions (Ising spins) of S = 1 and12 in the finite magnetic field is exactly solved by using the distribution function method. The magnetization process and the distribution of the thermal averages of the spins, which are of great interest in the random system, are discussed in detail for some mixtures. It is shown that the magnetization increases abruptly as soon as the magnetic field is applied even if all exchange integrals are antiferromagnetic and that the magnetization curve of the mixture having antiferromagnetic exchange integrals has some steps when T≈0. The origin of those features are discussed from the view points of the distribution of the thermal averages of the spins.