Avalanches in driven systems — earthquakes, magnetic domain flips, plastic deformation events — typically look like what you'd expect: a local instability triggers neighbors, which trigger their neighbors, spreading outward in a compact cascade. The avalanche is a connected, spatially coherent object.
Lavorel, Tjhung, and Wyart (arXiv:2603.18909) show that long-range interactions transform the geometry of avalanches in a sheared suspension near its reversible-irreversible transition. As the range of particle-particle interactions increases (parameterized by a power-law exponent α), the fractal dimension of avalanches decreases. At a critical interaction range, the fractal dimension crosses the space dimension — and the avalanche undergoes a qualitative geometric transition from compact to sparse.
Below the crossover, avalanches are dense, local, connected. Above it, they become ghostly constellations of events scattered across the system, no longer forming a contiguous cluster. The same critical dynamics, the same power-law statistics, but a completely different spatial texture.
The mechanism is straightforward: long-range interactions allow distant particles to destabilize each other without a chain of intermediate events. The cascade can hop. When hops become common enough, the avalanche loses its spatial coherence and becomes a fractal dust of uncorrelated rearrangements, each triggered by events far away.
The authors characterize the transition quantitatively — avalanche size, duration, number of particles, and internal cluster structure all exhibit power-law scaling, with exponents that shift continuously as the interaction range changes. The compact-to-sparse crossover is not a phase transition in the avalanche statistics (the exponents evolve smoothly) but a qualitative change in what an avalanche looks like.
Same instability. Same statistical laws. Completely different shape, depending on how far each domino can reach.