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Simple symmetry considerations would suggest that the transition from thesmectic-A phase to the long-range bond orientationally ordered hexaticsmectic-B phase should belong to the XY universality class. However, a numberof experimental studies have constantly reported over the past twenty years"novel" critical behavior with non-XY critical exponents for this transition.Bruinsma and Aeppli argued in Physical Review Letters {\bf 48}, 1625 (1982),using a $4-\epsilon$ renormalization-group calculation, that short-rangemolecular herringbone correlations coupled to the hexatic ordering drive thistransition first order via thermal fluctuations, and that the critical behaviorobserved in real systems is controlled by a `nearby' tricritical point. We haverevisited the model of Bruinsma and Aeppli and present here the results of ourstudy. We have found two nontrivial strongly-coupled herringbone-hexatic fixedpoints apparently missed by those authors. Yet, those two new nontrivialfixed-points are unstable, and we obtain the same final conclusion as the onereached by Bruinsma and Aeppli, namely that of a fluctuation-driven first ordertransition. We also discuss the effect of local two-fold distortion of the bondorder as a possible missing order parameter in the Hamiltonian.Comment: 1 B/W eps figure included. Submitted to Physical Review E. Contact:  gingras@gandalf.uwaterloo.c

physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics

Hexatic-herringbone coupling at the hexatic transition in smectic liquid crystals:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>4</mml:mn><mml:mo>−</mml:mo><mml:mi>ε</mml:mi></mml:math>renormalization group calculations revisited

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