Critical behavior at nematic–smectic-A1phase transtions. II. Preasymptotic three-dimensionalXYanalysis of x-ray andCpdata

X-ray data are reported for the nematic phase near the nematic (N)–smectic-${\mathit{A}}_1$(Sm-${\mathit{A}}_1$) transition in a binary mixture of pentylphenylcyanobenzoyloxy benzoate (${\mathrm{DB}}_5$CN)+cyanobenzoyloxypentylstilbene (${\mathrm{C}}_5$ stilbene). These data and x-ray data from four other N–Sm-${\mathit{A}}_1$ systems, plus the corresponding high-resolution ${\mathit{C}}_{\mathit{p}}$ data, are analyzed using the exact solutions of preasymptotic three-dimensional (3D) XY theory. The correlation volume ${\xi }_{\mathrm{\parallel }}$ ${\xi }_{\mathrm{\perp }}^2$, smectic susceptibility σ, and heat capacity ${\mathit{C}}_{\mathit{p}}$ are in good agreement with preasymptotic theoretical predictions. First-order corrections-to-scaling terms were known previously to be important for describing ${\mathit{C}}_{\mathit{p}}$; their importance for ${\xi }_{\mathrm{\parallel }}$ ${\xi }_{\mathrm{\perp }}^2$ and σ is demonstrated here. Many universal features of the 3D XY model are confirmed by the present self-consistent analysis, but the critical anisotropy of the individual lengths ${\xi }_{\mathrm{\parallel }}$ and ${\xi }_{\mathrm{\perp }}$ and the fact that ${\mathit{C}}_{\mathit{p}}$ exhibits a normal XY amplitude ratio rather than the theoretically predicted inverted ratio are still unresolved issues.