Layer fluctuations and hexatic order in liquid crystals

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Abstract
In the smectic-A and hexatic-B phases, the layers are not planar but undergo large fluctuations. In order to find the effect of these fluctuations on the smectic-A-hexatic-B transition, we construct a Ginzburg-Landau Hamiltonian in terms of the hexatic order parameter ψ and the layer fluctuations u. The fields ψ and u are coupled because of the geometrical frustration introduced by the curvature of the layers. We integrate out the u field to obtain an effective Hamiltonian in terms of ψ alone. This integration leads to a finite renormalization of the coefficients in the effective Hamiltonian. By this mechanism, layer fluctuations may drive the smectic-A-hexatic-B transition to be first-order if the hexatic stiffness constants are sufficiently large. This effect may be related to observed anomalies in the specific heat at that transition