Pure states in spin glasses

The question of the existence of multiple pure states in spin glasses and other disordered systems is considered. The authors show that the distribution of overlaps, P(q), is an unreliable indicator of how many distinct pure states a system has. They discuss the definition of, and possible relations between, pure states. They also discuss the spin glass on a Bethe lattice and the infinite-range model, pointing out why their ordered phases are likely to be unlike that of realistic spin glass models. Various possibilities for the behaviour of finite-range spin glasses are discussed.