Generic first-order nematic-isotropic phase transition of orientational phases with polyhedral symmetries

摘要

Polyhedral nematics are exotic orientational phases that possess a complexinternal symmetry and may be realized in colloidal and molecular liquid-crystalsystems. Although their classification has been known for a long time, theirphase transitions to isotropic liquids remain largely unexplored except for afew symmetries. In this work, we utilize a recently introduced non-Abeliangauge theory to explore the nematic-isotropic phase transition for allthree-dimensional polyhedral nematics. The gauge theory can readily be appliedto nematic phases with an arbitrary point-group symmetry, including those wheretraditional Landau methods and the associated lattice models may become tooinvolved to implement owing to a tensor order parameter of too high rank or(the absence of) mirror symmetries. From our Monte Carlo simulations, we findthat the nematic-isotropic transition is generically first-order for allpolyhedral symmetries. Moreover, we show that our results are consistent with arenormalization scenario, as well as with other lattice models for symmetriesalready studied in the literature. We argue that extreme fine tuning isrequired to promote those transitions to second order ones.