Abstract
Addressing the nature of an unexpected smectic-A' phase in liquid crystal 54COOBC films, we perform large scale Monte Carlo simulations of a coupled hexatic-nematic XY model. The resulting finite-temperature phase diagram reveals a small region with composite Potts $\mathbb{Z}_3$ order above the vortex binding transition; this phase is characterized by relative hexatic-nematic ordering though both variables are disordered. The system develops algebraic hexatic and nematic order only at a lower temperature. This multi-step melting scenario agrees well with the experimental observations of a sharp specific heat anomaly that emerges above the onset of hexatic positional order. We therefore propose that the smectic-A' phase is characterized by composite Potts order and bound-states of fractional vortices.
Highlights
Two-dimensional XY models have played a central role in the understanding of topology in statistical and condensed matter physics
Using large-scale parallel-tempering Monte Carlo simulations, we identify a small region where there is a sharp transition leading to Potts order even though the underlying hexatic and nematic angles remain disordered; quasi-long-range order (QLRO) in these variables develops at a lower temperature via a KT transition
LR order in the emergent Potts Z3 variable ni, as defined related to σi in Eq (4.4), exists even in a region with finiterange correlations of the hexatic and nematic degrees of freedom. This suggests that the hidden order phase that is experimentally observed in 54COOBC films is characterized by LR relative Potts order, and the sharp specific heat divergence is associated with a 2D Potts phase transition
Summary
Two-dimensional XY models have played a central role in the understanding of topology in statistical and condensed matter physics. Using large-scale parallel-tempering Monte Carlo simulations, we identify a small region where there is a sharp transition leading to Potts order even though the underlying hexatic and nematic angles remain disordered; quasi-long-range order (QLRO) in these variables develops at a lower temperature via a KT transition This emergent composite order, in which disordered nematic and hexatic angles order relative to each other, is a new member in the rich class of vestigial orders that has been identified as playing a key role in the phase diagrams of frustrated magnets [20–22,36–45], unconventional superconductors [28,29,46–53], ultracold atoms [54], and liquid crystals [55]. VI with concluding remarks and outlook for future research directions
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