Manna Sandpile — Stochastic SOC
The Manna model: grains accumulate until a site reaches threshold z≥2, then topples by sending one grain to each of 2 randomly chosen neighbors. Self-organized criticality produces power-law avalanche size distributions P(s) ~ s^{-τ} with τ≈1.27 (Manna universality class).
Physics: Unlike the deterministic Bak-Tang-Wiesenfeld sandpile (τ=1.0 in 2D, non-universal), the stochastic Manna model defines a true universality class. Sites topple when z≥2 by sending grains to two randomly chosen neighbors. This stochasticity breaks the deterministic parity symmetry, producing genuine critical exponents: τ≈1.27 (avalanche size), z≈1.51 (dynamic), d_f≈1.79 (fractal). The model is equivalent to critical spreading of activity in directed percolation with conservation.