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Using a high resolution Monte Carlo simulation technique based onmulti-histogram method and cluster-algorithm, we have investigated criticalproperties of a coupled XY model, consists of a six-fold symmetric hexatic anda three-fold symmetric herringbone field, in two dimensions. The simulationresults demonstrate a series of novel continues transitions, in which bothlong-range hexatic and herringbone orderings are established simultaneously. Itis found that the specific-heat anomaly exponents for some regions in couplingconstants space are in excellent agreement with the experimentally measuredexponents extracted from heat-capacity data near the smecticA-hexaticBtransition of two-layer free standing film

Emergence of hexatic and threefold hidden order in two-dimensional smectic liquid crystals: A Monte Carlo study