Jamming and replica symmetry breaking of weakly disordered crystals
Jamming and replica symmetry breaking of weakly disordered crystals
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DOI：
10.1103/physrevresearch.2.033220
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发表时间：
2019-10
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影响因子：
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通讯作者：
Harukuni Ikeda
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文献类型：
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作者：
Harukuni Ikeda
我们讨论了在干扰转变点附近具有小多分散性的晶体的物理性质。为此，我们引入了一个有效的单粒子模型，考虑到最近邻结构的晶体。在大维数的限制下，利用复型法可以解析地求解该模型。在不存在多分散性的情况下，复制对称解是稳定的，直到干扰转变点，这导致完美晶体的标准标度。相反，对于有限的多分散性，该模型经历了完整的副本对称性破缺（RSB）过渡之前的干扰过渡点。在RSB阶段，该模型表现出相同的缩放无定形固体附近的堵塞转变点。这些结果与最近对多分散性晶体的数值模拟完全一致。该模型的简单性也使我们能够推导出振动态密度的标度行为，这些行为可以在未来的实验和数值模拟中进行测试。
We discuss the physics of crystals with small polydispersity near the jamming transition point. For this purpose, we introduce an effective single-particle model taking into account the nearest neighbor structure of crystals. The model can be solved analytically by using the replica method in the limit of large dimensions. In the absence of polydispersity, the replica symmetric solution is stable until the jamming transition point, which leads to the standard scaling of perfect crystals. On the contrary, for finite polydispersity, the model undergoes the full replica symmetry breaking (RSB) transition before the jamming transition point. In the RSB phase, the model exhibits the same scaling as amorphous solids near the jamming transition point. These results are fully consistent with the recent numerical simulations of crystals with polydispersity. The simplicity of the model also allows us to derive the scaling behavior of the vibrational density of states that can be tested in future experiments and numerical simulations.