Kosterlitz-Thouless phase transitions in two-dimensional liquid crystals

A renormalization-group analysis, used by previous authors to study the critical properties of the two-dimensional ferromagnetic $x-y$ model, leads to a universal jump in the Franck constant of a two-dimensional nematic liquid crystal as the critical temperature is approached from below. The results obtained are different from those obtained for the $x-y$ model by previous authors because vortices of half-integral strength must be taken into account. Experimental implications of these results are discussed.