Thermal-Conductivity Studies near the Smectic-A-Hexatic-BTransition in a Liquid-Crystal Compound

High-resolution thermal-conductivity and heat-capacity studies on the same sample have been carried out near the smectic-$A$-hexatic-$B$ transition of $n-\mathrm{hexyl}-4\text{'}-n-\mathrm{pentyloxybiphenyl}-4-\mathrm{carboxylate}$ (65OBC). A power-law fitting with background contribution to the thermal conductivity anomaly leads to a dynamic critical exponent $a=0.51\mathrm{}$ and a ratio of critical amplitudes $\frac{{\Lambda }^{+}}{{\Lambda }^{-}}=0.93\mathrm{}$. We will discuss our results on the basis of a dynamic scaling. The thermal diffusivity shows a pronounced drop near the transition, which clearly demonstrates critical slowing down of the thermal fluctuations. mal fluctuations.