For a surface interaction linear in the order parameter and favoring an orientation in which liquid-crystalline molecules lie parallel to the surface (but which is independent of whether the orientation is uniaxial or isotropic in the bounding plane), a symmetry-breaking phase transition in a surface layer is possible at temperatures above that of the bulk isotropic to nematic transition. At the surface transition, the high-temperature in-plane isotropic state becomes unstable with respect to a biaxial phase, the transition being continuous and therefore of-the Berezinskii-Kosterlitz-Thouless (BKT) type, It is expected to occur for intermediate surface couplings but not at very weak or very strong couplings. The bulk phase always remains disordered. The BKT transition boundary is calculated explicitly and the results are compared with earlier theoretical studies on systems with linear or quadratic surface interaction potentials. Numerical estimates indicate that systems having the required linear surface potentials can be prepared and possible techniques for observing a BKT-type phase transition are discussed.
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