3DXYbehavior of a nematic-smectic-Aphase transition: Confirmation of the de Gennes model

A high-resolution x-ray study of the nematic--to--smectic A₁ phase transition of 8OPCBOB gives a critical exponent for the susceptibility {γ}=1.39±{}0.08, and for the parallel correlation length ν_∥=0.71±{}0.04. These values, as well as the known exponent of the heat capacity, agree with the predictions from the 3D-XY model. The different critical behavior of the perpendicular correlation length (ν_⊥=0.56±{}0.05) is shown to be related to the quartic term in q_⊥ present in the structure factor. Our analysis resolves a long-standing puzzle about the critical behavior of this phase transition.