Recent studies have shown that the melting of two-dimensional crystals can be either continuous or discontinuous, relying on multiple parameters such as particle stiffness, density, and particle size dispersity. However, what determines the continuity or discontinuity of the two-dimensional melting remains elusive. Here we study the two-dimensional melting of binary mixtures of soft-core particles. The two particle species are different in either particle size or particle stiffness. Starting with the mono-component systems which exhibit discontinuous hexatic–liquid transition, we gradually increase the particle size or stiffness dispersity and find that the hexatic–liquid coexistent region shrinks and eventually vanishes above a critical dispersity. Therefore, the growth of disorder caused by the particle size or stiffness dispersity leads to the discontinuous–continuous transition of the two-dimensional melting. We further find that as long as the melting is continuous the defect concentrations on the boundary between hexatic and liquid phases remain almost constant, accompanied by an almost constant correlation length. These characteristic defect concentrations and correlation length are universal and independent of particle interactions, temperature, and type of particle dispersity, which act as signatures of the continuous two-dimensional melting.

中文翻译：

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二维熔融过程中连续六方-液相转变的特征

最近的研究表明，二维晶体的熔化可以是连续的，也可以是不连续的，这取决于多个参数，例如颗粒刚度，密度和粒度分散度。但是，确定二维熔化的连续性或不连续性的因素仍然难以捉摸。在这里，我们研究了软核颗粒的二元混合物的二维熔化。两种颗粒的粒径或刚度都不同。从表现出不连续的六价液相过渡的单组分体系开始，我们逐渐增加了颗粒尺寸或刚度分散度，发现六价液相共存区域收缩并最终在临界分散度以上消失。所以，由粒度或刚度分散性引起的无序生长导致二维熔化的不连续-连续转变。我们进一步发现，只要熔化是连续的，在六方相和液相之间的边界上的缺陷浓度几乎保持恒定，同时伴随着几乎恒定的相关长度。这些特征缺陷浓度和相关长度是通用的，并且与粒子相互作用，温度和粒子分散性类型无关，而后者是连续二维熔化的特征。伴随着几乎恒定的相关长度。这些特征缺陷浓度和相关长度是通用的，并且与粒子相互作用，温度和粒子分散性类型无关，而后者是连续二维熔化的特征。伴随着几乎恒定的相关长度。这些特征缺陷浓度和相关长度是通用的，并且与粒子相互作用，温度和粒子分散性类型无关，而后者是连续二维熔化的特征。