Defect model of the smectic A-nematic phase transition

Abstract

It is shown that phase transitions in three dimensions breaking up an ordered state by polar defect lines can be modelled on the xy model, at least if the interaction of the lines is only steric. The analogy is established for a lattice model by means of a xy high-temperature expansion for spin 1/2. The defect model is applied to the smectic A-nematic transition which is interpreted as a breakup of order by smectic dislocation loops. Critical director fluctuations at T < Tc are explained as a manifestation of these loops. Critical behaviour is shown to differ from that of the conventional xy model because of the peculiar elastic interaction of smectic dislocations