Bond orientational order in smectic liquid crystals

Order in the orientations of bond angles in bulk smectic liquid crystals is investigated. A simple model which couples in-plane bond orientations to a tilt degree of freedom is solved in the mean-field approximation. In addition to the usual smetic-$A$ and smetic-$C$ phases, there is an untilted hexatic phase, with long-range order in the bond angles. Modifications of the meanfield theory due to fluctuations are determined, with the aid of results from the $\epsilon =4-d$ expansion. Induced sixfold bond-angle order in smectic-$C$ liquid crystals vanishes rapidly near the smectic-$C$ to smectic-$A$ transition temperature, as ${|T-T_c|}^{{\beta }_6}$, where ${\beta }_6\approx 3.59$. A form for the coupling of bond orientational order to density fluctuations is proposed.