A transition from a square to a hexagonal lattice is studied in a 2D system of particles interacting via a core-softened potential. Due to the presence of two length scales of repulsion, different local configurations with four, five, and six neighbors are possible, leading to the formation of complex crystals. The previously proposed interpolation method is generalized to calculate pair correlations in crystals whose unit cell consists of more than one particle. The high efficiency of the method is illustrated using a snub square lattice as a representative example. Molecular dynamics simulations show that the snub square lattice is broken upon heating, generating a high-density quasicrystalline phase with 12-fold symmetry (HD12 phase). A simple theoretical model is proposed to explain the physical mechanism responsible for this phenomenon: with an increase in the density (from square to hexagonal phases), the concentrations of different local configurations randomly realized through a plane tiling change, which minimizes the energy of the system. The calculated phase diagram in the intermediate density range justifies the existence of the HD12 phase and demonstrates a cascade of first-order transitions “square – HD12 – hexagonal” solid phases with increasing density. The results allow us to better understand the physical mechanisms responsible for the formation of quasicrystals, and, therefore, should be of interest for broad community in materials science and soft matter.

中文翻译：

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二维核软化系统中的复杂晶体结构

在通过粒子相互作用的2D系统中研究了从正方形到六边形晶格的过渡核心软化潜力。由于存在两个排斥的长度尺度，因此具有四个，五个和六个邻居的不同局部配置是可能的，从而导致形成复杂的晶体。普遍采用先前提出的插值方法来计算其晶胞由一个以上粒子组成的晶体中的对相关性。以小巧方格为代表的例子说明了该方法的高效率。分子动力学模拟表明，冷压方格在加热时会破裂，从而生成具有12倍对称性的高密度准晶相（HD12相）。提出了一个简单的理论模型来解释造成这种现象的物理机制：随着密度的增加（从方相到六方相），通过平面平铺变化随机实现的不同局部配置的集中，从而最大程度地减少了系统的能量。计算得出的中等密度范围内的相图证明了HD12相的存在，并证明了随着密度增加，一阶跃迁“正方形-HD12-六角形”固相的级联。结果使我们能够更好地理解造成准晶体形成的物理机制，因此，应该引起材料科学和软物质领域的广泛关注。计算出的中等密度范围内的相图证明了HD12相的存在，并证明了随着密度增加，一阶跃迁“正方形-HD12-六角形”固相的级联。结果使我们能够更好地理解造成准晶体形成的物理机制，因此，应该引起材料科学和软物质领域的广泛关注。计算出的中等密度范围内的相图证明了HD12相的存在，并证明了随着密度增加，一阶跃迁“正方形-HD12-六角形”固相的级联。结果使我们能够更好地理解造成准晶体形成的物理机制，因此，应该引起材料科学和软物质领域的广泛关注。