Emergent marginality in frustrated multistable networks

We study disordered networks of coupled bistable elastic elements, representing a coarse-grained view of amorphous solids. We find that such networks self-organize to a marginally stable state, in which the barrier for local activations becomes vanishingly small. The model provides unique access to both local and global properties associated with marginal stability. We directly measure pseudo-gaps in the spectrum of local excitations, as well as diverging fluctuations under shear. Crucially, the dynamics are dominated by a small population of bonds that are locally unstable, which give rise to quasi-localized, low-frequency vibrational modes and scale-free avalanches of instabilities. We propose a correction to the scaling between the pseudo-gap exponent and avalanche statistics based on diverging length fluctuations. Our model combines a coarse-grained view with a continuous, real-space implementation, providing novel insights to a wide class of amorphous solids.