Abstract
The in-plane projection of the director in smectic-C liquid crystals and the hexatic order parameter in hexatic smectic liquid crystals are both analogous to the magnetization in an XY ferromagnet. Recent experimental results and theoretical arguments suggest that two-dimensional XY ferromagnets have a universal finite-size-induced effective magnetization exponent \ensuremath{\beta}\ensuremath{\approxeq}0.23 [S. T. Bramwell and P. C. W. Holdsworth, J. Phys. Condens. Matter 5, L53 (1993)]. From these results, we predict that XY-like order parameters in thin free-standing smectic liquid-crystal films should behave as \ensuremath{\propto}(${\mathit{T}}_{\mathit{C}}$-T${)}^{\mathrm{\ensuremath{\beta}}}$ in an intermediate temperature range below the relevant transition temperature ${\mathit{T}}_{\mathit{C}}$ if they exhibit a Kosterlitz-Thouless transition of a single XY-like order parameter.
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More From: Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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