THIS TALK IS CANCELLED.
Intermediate phases with “vestigial order” occur when the spontaneously broken symmetries of a “fully ordered” groundstate are restored sequentially as a function of increasingly strong thermal or quantum fluctuations, or of increasing magnitude of quenched randomness. As an important example, incommensurate charge-density-wave short-range order ( i.e. with a finite correlation length) and a sharp phase transition to a phase with long-range nematic order is shown to be natural in the presence of weak quenched disorder in systems which, in the absence of disorder, would have unidirectional (stripe) ordered ground states. Recent experiments probing charge order in the pseudo-gap regime of the hole-doped cuprate high-temperature superconductors and nematic order in the Fe based superconductors are interpreted in light of these results.