Smectic-glass transition in a liquid-crystal cell with a "dirty" substrate

We explore the smectic liquid-crystal order in a cell with a "dirty" substrate imposing random pinnings. Within harmonic elasticity we find a subtle three-dimensional surface disorder-driven transition into a pinned smectic glass, controlled by a three-dimensional Cardy-Ostlund-like fixed line, akin to a super-rough phase of a two-dimensional xy model. We compute the associated random substrate-driven distortions of the smectic-glass state, identify the characteristic length scales on the heterogeneous substrate and in the bulk, and discuss a variety of experimental signatures. Copyright (C) EPLA, 2012