# Defect-mediated melting and new phases in three-dimensional systems with a single soft direction

## Abstract

We construct a theory, based on defect unbinding, of the m=1, d=3 XY Lifshitz point. This theory also describes phase transitions in three-dimensional systems with layered ordered phases in which the layer normals are energetically confined to a predetermined plane. Such systems include smectics-A with negative magnetic (dielectric) anisotropy and smectics-C and cholesterics with positive magnetic (dielectric) anisotropy in external magnetic (electric) fields, smectics-A and -CI, and various magnetic systems with spatially modulated phases. We show that this class of systems can disorder via two continuous transitions, in which case a bond-orientationally-ordered phase intervenes between the low-temperature, translationally ordered and high-temperature, translationally disordered phases. The transition between the bond orientationally ordered and isotropic phases is in the universality class of the isotropic d=3 XY model. The transition from the translationally ordered phase to the orientationally ordered phase is in the universality class of the m=1, d=3 XY Lifshitz point, which exhibits anisotropic scaling with two distinct correlation length exponents? and S. Duality arguments show that either (a)?/S=(2/3) or (b) the transition is self-dual, in which case the specific-heat amplitude ratio is unity. © 1986 The American Physical Society.