Theory of disordered spin systems

Disordered, i.e. , containing random parameters, lattice spin systems are considered. It is shown that the free energy in the macroscopic limit becomes nonrandom if the probability distribution of the random parameters satisfies conditions of spatial homogeneity on the average and vanishing of statistical correlations at distant points. The possible orientations of the spins in these systems are discussed in terms of random fields. An asymptotically exactly solvable model of such a system is proposed; it demonstrates different types of orientation, including one corresponding to the spin glass state in which there is no macroscopic magnetization but the magnetic moment of individual regions of the crystal is nonzero.