Jamming and replica symmetry breaking of weakly disordered crystals

Harukuni Ikeda

doi:10.1103/physrevresearch.2.033220

Abstract

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.

Highlights

Physics of crystal and amorphous solids are qualitatively different
We focus on the jamming of spherical and frictionless particles interacting with finite and repulsive potentials
The behavior of G is directly related to the contact number per particle Z as G ∝ δZ ≡ Z − Ziso [11]

Summary

Introduction

Physics of crystal and amorphous solids are qualitatively different. For instance, low frequency eigenmodes of crystals are phonon, and the vibrational density of states D(ω) follows the Debye law D(ω) ∼ ωd−1, where d denotes the spatial dimensions [1]. The density of states normalized by the Debye’s prediction D(ω)/ωd−1 shows a peak at a certain frequency ω = ωBP [2,3,4,5,6] This phenomenon is known as the boson peak and thought to be one of the universal properties of amorphous solids [7]. Crystal and amorphous solids show distinct elastic properties near the (un) jamming transition point at which constituent particles lose contact, and simultaneously the pressure vanishes [8]. G of amorphous solids shows the power law behavior G ∼ p1/2 and vanishes at the jamming transition point [8,9]. At the jamming transition point, δZ > 0 for perfect crystals, leading

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Conclusion