Exact Results for Spatiotemporal Correlations in a Self-Organized Critical Model of Punctuated Equilibrium

We introduce a self-organized critical model of punctuated equilibrium with many internal degrees of freedom ( $M$) per site. We find exact solutions for $M\to \infty$ of cascade equations describing avalanche dynamics in the steady state. This proves the existence of simple power laws with critical exponents that verify general scaling relations for nonequilibrium phenomena. Punctuated equilibrium is described by a devil's staircase with a characteristic exponent ${\tau }_{\mathrm{first}}=2-d/4$ where $d$ is the spatial dimension.