Hexatic-herringbone coupling at the hexatic transition in smectic liquid crystals: 4-ε renormalization group calculations revisited

Simple symmetry considerations would suggest that the transition from the smectic-A phase to the long-range bond-orientationally ordered hexatic smectic-B phase should belong to the XY universality class. However, a number of experimental studies have reported over the past twenty years “novel” critical behavior with non-XY critical exponents for this transition. Bruinsma and Aeppli argued [Phys. Rev. Lett. 48, 1625 (1982)], using a 4-ε renormalization-group calculation, that short-range molecular herringbone correlations coupled to the hexatic ordering drive this transition first order via thermal fluctuations, and that the critical behavior observed in real systems is controlled by a “nearby” tricritical point. We have revisited the model of Bruinsma and Aeppli and present here the results of our study. We have found two nontrivial strongly coupled herringbone-hexatic fixed points apparently missed by these authors. Yet, these two nontrivial fixed points are unstable, and we obtain the same final conclusion as the one reached by Bruinsma and Aeppli, namely that of a fluctuation-driven first-order transition. We also discuss the effect of local twofold distortion of the bond order as a possible “extra” order parameter in the Hamiltonian.