Theory of the anomalous critical behavior for the smectic-$A$–hexatic transition

We propose a theoretical explanation for the long-standing problem of the anomalous critical behavior of the heat capacity near the smectic-$A$–hexatic phase transition. Experiments find a large specific heat critical exponent $\alpha =0.5–0.7$, which is inconsistent with a small negative value $\alpha \approx -0.01$ expected for the three-dimensional $XY$ universality class. We show that most of the observed features can be explained by treating simultaneously fluctuations of the hexatic orientational and translational (positional) order parameters. Assuming that the translational correlation length ${\xi }_{tr}$ is much larger than the hexatic correlation length ${\xi }_h$, we calculate the temperature dependence of the heat capacity in the critical region near the smectic-$A$–hexatic phase transition. Our results are in quantitative agreement with the calorimetric experimental data.

Figure 1

Calorimetric experimental data [17] for 65OBC (open circles) versus our calculation (solid line)