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

A high-resolution x-ray study of the nematic–to–smectic ${\mathit{A}}_1$ phase transition of 8OPCBOB gives a critical exponent for the susceptibility γ=1.39±0.08, and for the parallel correlation length ${\nu }_{\mathrm{\parallel }}$=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 (${\nu }_{\mathrm{\perp }}$=0.56±0.05) is shown to be related to the quartic term in ${\mathit{q}}_{\mathrm{\perp }}$ present in the structure factor. Our analysis resolves a long-standing puzzle about the critical behavior of this phase transition.