We explore the link between the melting scenarios of two-dimensional systems of hard disks and squares through replica-exchange Monte Carlo simulations of hard superdisks. The well-known melting scenarios are observed in the disk and square limits, while we observe an unusual three-step scenario for dual shapes. We find that two mesophases mediate the melting: a hexatic phase and another fluid phase with a $D_2$ local symmetry, we call it rhombatic, where both bond and particle orientational orders are quasi-long-range. Our results show that not only can the melting process of liquid-crystal forming molecules be complicated, where elongated shapes stabilize several mesophases, but also that of anisotropic quasispherical molecules.

中文翻译：

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二维超硬磁盘的三步熔化

我们通过硬盘超级磁盘的副本交换蒙特卡洛模拟研究了二维硬盘系统和正方形的熔化场景之间的联系。在圆盘和正方形极限中观察到了众所周知的熔化情况，而对于双重形状，我们观察到了不寻常的三步情况。我们发现两个中间相介导了熔化：一个六相和另一个具有$d_2$局部对称，我们称其为菱形，其中键和粒子的取向顺序均为准远距离。我们的结果表明，不仅液晶形成分子的熔融过程复杂化（其中细长的形状稳定了多个中间相），而且各向异性的准球形分子的熔融过程也变得复杂。