Universality and Nonuniversality in Frustrated Smectics

Abstract

When the idea that incommensurability problems might exist in smectics was first put forward [1], the wealth of consequences was not guessed. The possibility of incommensurate smectics and the connection with reentrance was soon realized [2], but the understanding that antiphases were also a natural consequence of incommensurability [3] had to await their experimental discovery [4]. A total of at least seven different phases results from the simple introduction of two order parameters with two incommensurate preferred wave vectors [5]. In most cases, the stability domains of the different phases which can be obtained from the mean field agree well with experimental findings [6–8]. In the following we concentrate on those cases which cannot be simply described by the mean field approach. Curiously they seem a priori simpler since they do not involve phases other than nematics and smectics. However, rotational invariance and dislocation statistics provide enough input to bring novelty into the statistical physics of these problems. In this short note we outline the main features of the smectic A-smectic A transition [9,10] and its alternative, the “nematic island”, and discuss the degree of universality of the related phase diagrams.