Critical properties of two-dimensional random ising systems

Tsuguhiro Tamaribuchi

Viktoria Blavatska, Yurij V. Holovatch

Fumitaka Matsubara

The susceptibilities of both the one-dimensional random Ising chain and the random Ising Bethe lattice composed of plural kinds of magnetic atoms of S = 1/2 and non-magnetic atoms are studied based on a new method, i.e., by using simultaneous linear equation of order n, where n is the number of kinds of magnetic atoms. The susceptibilities of the binary and ternary systems, which correspond to n = 1 and 2, respectively, are exactly obtained for both the one-dimensional chain and the Bethe lattice. The critical temperature of the random Bethe lattice is also obtained. It is shown that the critical temperature of the binary Bethe lattice is in agreement with that of the ordinary two- or three-dimensional lattice in the cluster variation method and that the critical temperature of the ternary Bethe lattice is independent of the signs of exchange integrals. It is also conjectured that the critical temperature of the ordinary ternary system does not depend on the signs of exchange integrals when two kinds of magnetic atoms are of the same type and the lattice structure is loose-packed. The problem of the random exchange integrals is also discussed.

Andrzej Pękalski

Using the high-temperature series expansion method the critical temperature and critical index gamma for a system consisting of a random mixture of Ising and Heisenberg couplings have been estimated. It has been found that gamma as a function of concentration p of Heisenberg-type bonds has a minimum the location of which depends strongly on the ratio of the Ising to Heisenberg coupling constants. It is conjectured that this might correspond to a change in the character of the transition.

Jacques Villain, Thomas Nattermann, Moshe Schwartz

B. N. Shalaev