New ways are discussed of numerically detecting the nature of phase transitions and the position of phase equilibria in models of thermotropic and lyotropic liquid crystals where the phase transitions are dominated by strong fluctuations. The cases of continuous transitions (critical points), first-order transitions, as well as the absence of transitions, are considered. It is shown how computer-simulation techniques, which operate on a free-energy level by using reweighting (histogram) techniques in combination with finite-size scaling theory, provide an effective tool for unambiguously determining the nature of the transition and the position of associated phase equilibria. Three specific models are considered: the Lebwohl–Lasher model of the nematic–isotropic transition in thermotropic liquid crystals, the mismatch model of the main chain-melting phase transition in lipid-bilayer lyotropic liquid crystals, and a model for critical mixing in a lipid-bilayer lyotropic liquid crystal incorporated with trans-bilayer polypeptides.
High resolution X-ray diffraction study of Smectic A - Smectic A phase transitions in a binary mixture of polar thermotropic liquid crystals