Critical and Tricritical Behavior at the Nematic to Smectic-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>Transition

Abstract

High-resolution x-ray scattering measurements of the nematic to smectic-$A$ transitions in two different homologous series are reported; it is found that the correlation-length exponents ${\ensuremath{\nu}}_{\ensuremath{\parallel}}$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}$ and the susceptibility exponent $\ensuremath{\gamma}$ decrease continuously with decreasing nematic range; the transitions ultimately become first order. The exponents at the crossover point are close, but not identical, to mean-field tricritical values. For both series and all samples ${\ensuremath{\nu}}_{\ensuremath{\parallel}}\ensuremath{\ne}{\ensuremath{\nu}}_{\ensuremath{\perp}}$ while $\ensuremath{\alpha}+{\ensuremath{\nu}}_{\ensuremath{\parallel}}+2{\ensuremath{\nu}}_{\ensuremath{\perp}}\ensuremath{-}2=0$ to within the errors.