We examine the fluctuation-induced interaction energy Δf between the surfaces of a layered hexatic film within a quadratic-functional-integral approach. Both discrete and continuum formulations are studied. We find large corrections to the asymptotic behavior Δf(l)∝${\mathit{l}}^{\mathrm{-}2}$ for finite l, where l is the film thickness. A small field becomes relevant beyond a length scale ξ(h), while an enhanced surface Frank constant is irrelevant above a length ξ(K). Possible relevance of these results to recent experiments on layer-by-layer surface ordering in liquid-crystal films is discussed.

• Received 1 February 1993

DOI:https://doi.org/10.1103/PhysRevE.47.3456