An upper-bound on the discontinuity at the smectic A-nematic phase transition in octylcyanobiphenyl (8CB): A high-resolution birefringence study

Although the nematic-smectic $A$ ($N$-Sm$A)$ transition in liquid crystals (LCs) has been extensively studied, it is still quite controversial. Most theoretical studies predict that the transition should be of 3-dimensional (3D) XY type. However, the experimental results to date have not established a clear case of 3D \textit{XY} universality. Halperin, Lubensky and Ma (HLM) predicted that the crossover should always make the $N$-Sm$A$ transition first order with very small latent heats. HLM-type first order N-Sm$A$ transitions has been evidenced by ASC data, but inconsistencies remain in reported discontinuity values. Of particular relevance is pure 8CB LC with an estimated HLM contribution substantially smaller than the upper limit for the latent heat from ASC. We carried out high-resolution birefringence measurements near the N-Sm$A $transition of 8CB LC. We find that the Sm$A$-$N $phase transition is continuous. For a possible discontinuity in the $N$ order parameter $S(T)$ at $T_{AN}$ we obtain an upper limit of 0.0002, which is consistent with the ASC latent upper limit and HLM theory. The temperature derivative of $S(T)$ exhibits a power law divergence with a critical exponent that is consistent with $\alpha $ $=$ 0.31 $\pm$ 0.03 obtained from ASC.