For a surface interaction quadratic in the magnitude of the order parameter and favoring an in-plane molecular orientation, it is shown that a nematic surface state with quasi-two-dimensional order can exist in a narrow temperature range above the bulk transition point. This phase is characterized by fully biaxial order and the transition between it and the fully disordered one is via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. The BKT transition temperature is calculated as are the elastic and inelastic light-scattering intensities. The latter is a possible technique for observing the transition and confirming its BKT character. Numerical estimates indicate that systems having the surface interactions required to exhibit this type of nematic phase transition can be prepared. PACS number(s): 64.70.Md, 68.35.Rh, 61.30.v

We propose a theoretical explanation for the long-standing problem of the anomalous critical behavior of the heat capacity near the smectic-A-hexatic phase transition. Experiments find a large specific heat critical exponent α=0.5-0.7, which is inconsistent with a small negative value α≈-0.01 expected for the three-dimensional XY universality class. We show that most of the observed features can be explained by treating simultaneously fluctuations of the hexatic orientational and translational (positional) order parameters. Assuming that the translational correlation length ξ_{tr} is much larger than the hexatic correlation length ξ_{h}, we calculate the temperature dependence of the heat capacity in the critical region near the smectic-A-hexatic phase transition. Our results are in quantitative agreement with the calorimetric experimental data.