Smectic liquid crystals in random environments

We study smectic liquid crystals in random environments, e.g., aerogel. A l ow-temperature analysis reveals that even arbitrarily weak quenched disorde r (i.e., arbitrarily low aerogel density) destroys translational (smectic) order, in agreement with recent experimental results. A harmonic approximat ion to the elastic energy suggests that there may be no ''smectic Bragg gla ss" phase in this system: even at zero temperature, it is riddled with disl ocation loops induced by the quenched disorder. This result would imply the destruction of orientational (nematic) order as well, and that the thermod ynamically sharp nematic-smectic transition is destroyed by disorder. We sh ow, however, that the anharmonic elastic terms neglected in the above appro ximate treatment are important (i.e., are "relevant" in the renormalization group sense), and may, indeed, stabilize the smectic Bragg glass and the s harp phase transition into it. However, they do not alter our conclusion th at translational (smectic) order is always destroyed. In contrast, we expec t that weak annealed disorder should have no qualitative effects on the sme ctic order. [S0163-1829(99)09121-3].