Long-Range Angular Correlations of Particle Displacements at a Plastic-to-Elastic Transition in Jammed Amorphous Solids

Understanding how a fluid turns into an amorphous solid is a fundamental challenge in statistical physics, during which no apparent structural ordering appears. In the athermal limit, the two states are connected by a well-defined jamming transition, near which the solid is marginally stable. A recent mechanical response screening theory proposes an additional transition above jamming, called a plastic-to-elastic transition here, separating anomalous and quasielastic mechanical behavior. Through numerical inflation simulations in two dimensions, we show that the onsets of long-range radial and angular correlations of particle displacements decouple, occurring, respectively, at the jamming and plastic-to-elastic transitions. The latter is characterized by a power-law diverging correlation angle and a power-law spectrum of the displacements along a circle. This work establishes two-step transitions on the mechanical properties during "decompression melting" of an athermal overjammed amorphous solid, reminiscent of the two-step structural melting of a crystal in two dimensions. In contradistinction with the latter, the plastic-to-elastic transition exists also in three dimensions.