Chapter 16
Quantum spin glasses

In this last chapter, we move beyond the simplest disordered models considered in Chapter 15, and consider systems which have magnetically ordered states which are rather more complicated than those in which the average moments are in a regular arrangement. In the context of the Ising/rotor models, such states can be obtained by allowing the exchange constants to randomly fluctuate over both negative and positive values. In particular, we will be interested here in the magnetically-ordered ``spin-glass'' state in which orientation of the spontaneous moment varies randomly from site to site, with a vanishing average over sites, [szi ] = 0 (or [ ni ] = 0-the square brackets represent an average over sites); such states are clearly special to disordered systems. For classical spin systems, such ordered states have been reviewed at length elsewhere [7,22,72]. The structure of the ordered spin-glass phases of quantum models is very similar, and so this shall not be the focus of our interest here. Rather, we are interested in the quantum phase transition from the spin glass to a quantum paramagnet, and the nature of the finite temperature crossovers in its vicinity, where quantum mechanics plays a more fundamental role.

The quantum Ising/rotor models of Part 2 also form the basis of much of our discussion of quantum spin glasses. However, in parallel, we also consider the appearance of spin-glass order in the metallic systems of Chapter 12. So one of our interests is the transition from a paramagnetic Fermi liquid to a spin density glass state: such a state is characterized by the analog of the order parameter for the ordinary spin density wave state, but now the orientation and magnitude of the amplitude varies randomly in space, along with random phase offsets.