Spin glass with non-random interactions

Abstract

Magnetic systems are investigated and a few exact results are obtained. Exact solutions are possible because the distribution of ferro- and antiferromagnetic bonds is assumed to obey certain rules, instead of being completely random. The ground state however, has the character of a spin glass. Two of the models have no phase transition in the case of one-dimensional (Ising) spins, whereas there is a phase transition for two-dimensional (XY) spins. The phase transition disappears again for high values of the spin dimensionality n. In a particular case of a three-dimensional, XY model, the susceptibility has been calculated at high and low temperatures; it has a maximum at some temperature, but a speculative argument is given that there is actually no kink.