Long-range angular correlations of particle displacements at a plastic-to-elastic transition in jammed amorphous solids

TL;DR

This study investigates the mechanical transition in jammed amorphous solids, revealing two distinct transitions characterized by long-range correlations and diverging angles, with implications for understanding the flow-to-solid transformation.

Contribution

It demonstrates the decoupling of radial and angular correlations at different transitions and confirms the plastic-to-elastic transition in three dimensions.

Findings

Long-range correlations emerge at jamming and plastic-to-elastic transitions.

Angular correlation diverges with a power-law at the plastic-to-elastic transition.

Displacement spectrum follows a power-law behavior along a circle.

Abstract

Understanding how a flow 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 quasi-elastic 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 over-jammed 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.