Extended isotropic-to-anisotropic crossover above the nematic–smectic-Aphase transition

We perform a one-loop, self-consistent calculation of the density-wave and director fluctuations above the nematic–smectic-A phase transition, find the renormalization of the perependicular and parallel correlation lengths, and for the first time calculate values of the anisotropic critical-point exponents ${\nu }_{\mathrm{\parallel }}$ and ${\nu }_{\mathrm{\perp }}$. As the transition is approached several distinct regions of scaling behavior are found with increasingly anisotropic critical behavior. A plot of effective exponents from experiment versus the anisotropy ratio ${\nu }_{\mathrm{\parallel }}$/${\nu }_{\mathrm{\perp }}$ reveals a systematic correlation that agrees with our calculation.