We report the structure of transient fluctuations in the liquid phase of a two-dimensional system that exhibits several ordered phases with different symmetries. The density-temperature phase diagram of the system studied, composed of particles with a repulsive shouldered soft-core pair interaction, has regions with stable liquid and hexatic phases, a square solid phase, two separate hexagonal solid phases, and a quasi-crystalline phase with 12-fold symmetry. We have examined the character of the structured fluctuations by computing the same-time aperture cross correlation function of particle configurations in several fluid regions near to and far from phase transition lines. The two primary goals of our study are (1) determination if the spectrum of structures of the fluctuations in the liquid is broader than or limited to the motifs exhibited by the ordered phases supported by the system and (2) determination of the density domains in the liquid that support particular transient structured fluctuations. In the system studied, along a low-temperature isotherm in the temperature-density plane that intersects all the ordered phases we find that the liquid phase exhibits structured fluctuations with hexagonal symmetry near both liquid-hexatic transition lines. Along the same isotherm and in the stable liquid between the lower density hexatic-to-liquid and the higher density liquid-to-square solid transitions, we find that transient hexagonal ordered fluctuations dominate the liquid region near the hexatic-to-liquid transition and square ordered fluctuations dominate the liquid region near the liquid-to square solid transition, but both of these structured fluctuations occur at all densities between these transition lines. At a higher temperature, at phase points in the liquid above, but close to the density maximum of an underlying transition, there are ordered fluctuations that can be correlated with the structure of the lower temperature phase. Although it is expected that very close to a liquid-ordered phase boundary a structured fluctuation in the liquid will have the same symmetry as the ordered phase, it is not obvious that structured fluctuations in thermodynamic states deep in the liquid phase will be similarly restricted. The most striking result of our calculations is that no evidence is found in the liquid phase for structured fluctuations with other symmetries than those of the ordered phases of the system.

中文翻译：

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具有多个有序相位的二维系统中的瞬态结构性涨落

我们报告二维系统的液相中的瞬态波动的结构，该系统表现出几个具有不同对称性的有序相。所研究系统的密度-温度相图由具有排斥性软核对相互作用的颗粒组成，具有稳定的液相和六相，正方形固相，两个单独的六方固相和准结晶相的区域具有12倍对称性。我们通过计算在接近和远离相变线的几个流体区域中粒子构型的同时孔径互相关函数来检查结构性波动的特征。我们研究的两个主要目标是（1）确定液体波动结构的光谱是否宽于或限于系统支持的有序相所显示的图案，以及（2）确定液体中的密度域支持特定的瞬时结构性波动的液体。在所研究的系统中，沿着与所有有序相相交的温度密度平面中的低温等温线，我们发现液相在两条液-六相转变线附近均表现出具有六边形对称性的结构性波动。沿着相同的等温线，在较低密度的六边形到液体和较高密度的液体到正方形的固体过渡之间的稳定液体中，我们发现瞬态六边形有序涨落主导着六边形到液体过渡附近的液体区域，而方形有序起伏主导着从液体到正方形固体过渡附近的液体区域，但是这两个结构性波动都发生在这些过渡线之间的所有密度。在较高的温度下，在上方液体中的相点处，但接近基本转变的密度最大值，存在有序的波动，这些波动可与较低温度的相的结构相关。尽管预期非常接近于液相有序相边界，液体中的结构性波动将与有序相具有相同的对称性，但是显然，液相深处的热力学状态的结构性波动将受到类似的限制。