Conservation laws, anisotropy, and ‘‘self-organized criticality’’ in noisy nonequilibrium systems

It is argued in the context of noisy, nonequilibrium Langevin models that systems with conserving deterministic dynamics and noise which violates the conservation law always exhibit self-organized criticality---spatial and temporal correlations that decay algebraically under generic conditions. Systems with both conserving deterministic dynamics and conserving noise require spatial anisotropy to exhibit self-organized criticality.