Commensurate-incommensurate transition with frozen impurities

Abstract

A model of commensurate-incommensurate transition with frozen impurities is discussed. In D = 3 dimensions the Bragg peak shift varies linearly with the chemical potential or temperature near the transition. At the lower critical dimension D, = 2, the commensurate phase is, strictly speaking, always instable. There is some analogy with an Ising model in random fields, where Dl is claimed to be 3 according to recent work. The replica trick is shown to be difficult to apply.