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.
Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition
New ordered phases in a class of generalized XY models
众所周知，二维XY模型表现出不寻常的无限级相变，属于Kosterlitz-plasterless（KT）普适类。在XY哈密顿量中引入一个耦合导致了伊辛普适类中的一个额外的相变[D. H. Lee和G. Grinstein，Phys. Rev. Lett. 55，541（1985）]。使用广泛的蒙特卡罗模拟和有限尺寸标度相结合，我们表明，高次谐波导致一个定性不同的相图，与额外的有序相源于铁磁和磁耦合之间的竞争。新的相变属于二维Potts，Ising或KT普适类。
