It has been well established that particulate systems show the jamming transition and critical scaling behaviors associated with it. However, our knowledge is limited to (nearly) monodisperse systems. Recently, a binary mixture of jammed particles with large size dispersity was studied, and it was suggested that two distinct jammed phases appeared. Here, we conduct a thorough numerical study on this system with a special focus on the statistics of and finite-size effects on the fraction of small particles that participate in the rigid network. We present strong evidence that two distinct jammed phases appear depending on the pressure and composition of two species, which are separated by the first-order phase transition. In one of two phases, only large particles are jammed, whereas both small and large particles are jammed in the other phase. Interestingly, the finite size scaling shows the transition is similar to the first-order transition in the random-field Ising model. We also describe the phase diagram in the pressure-composition plane, where the first-order phase transition line terminates at a critical point. In addition, we investigate the mechanical properties in terms of the elastic moduli over the phase diagram and find that discontinuous changes in elastic moduli emerge across the phase transition. Finally, we show the scaling laws of the elastic moduli in each jammed phase are not in consistent with those in the monodisperse systems.

中文翻译：

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大尺寸分散的阻塞颗粒的二元混合物中的相变

已经充分确定的是，微粒系统显示出干扰过渡和与之相关的临界结垢行为。但是，我们的知识仅限于（几乎）单分散体系。近来，研究了具有大尺寸分散性的堵塞颗粒的二元混合物，并且表明出现了两个不同的堵塞相。在这里，我们对这个系统进行了彻底的数值研究，特别是对参与刚性网络的小颗粒的分数的统计和有限大小的影响。我们提供有力的证据，根据两种物质的压力和成分，出现了两个不同的阻塞相，它们被一阶相变所分隔。在两相中的一个相中，只有大颗粒被阻塞，而在另一个相中，大颗粒和小颗粒都被阻塞。有趣的是，有限尺寸缩放显示过渡与随机场Ising模型中的一阶过渡相似。我们还描述了压力组成平面中的相图，其中一阶相变线终止于临界点。此外，我们根据相图上的弹性模量研究了机械性能，发现在相变过程中出现了弹性模量的不连续变化。最后，我们显示了在每个阻塞相中弹性模量的定律与单分散系统中的定律不一致。一阶相变线终止于临界点。此外，我们根据相图上的弹性模量研究了机械性能，发现在相变过程中出现了弹性模量的不连续变化。最后，我们显示了在每个阻塞相中弹性模量的定律与单分散系统中的定律不符。一阶相变线终止于临界点。此外，我们根据相图上的弹性模量研究了机械性能，发现在整个相变过程中出现了弹性模量的不连续变化。最后，我们显示了在每个阻塞相中弹性模量的定律与单分散系统中的定律不符。