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We study stability and distortions of liquid crystal nematic order in a cellwith a random heterogeneous substrate. Modeling this system as a bulk xy modelwith quenched disorder confined to a surface, we find that nematic order ismarginally unstable to such surface pinning. We compute the length scale beyondwhich nematic distortions become large and calculate orientational correlationfunctions using the functional renormalization-group and matching methods,finding universal logarithmic and double-logarithmic distortions in two andthree dimensions, respectively. We extend these results to a finite-thicknessliquid crystal cell with a second homogeneous substrate, detailing crossoversas a function of random pinning strength and cell thickness. We conclude withanalysis of experimental signatures of these distortions in a conventionalcrossed-polarizer-analyzer light microscopy.

Stability and distortions of liquid crystal order in a cell with a heterogeneous substrate