CONCEPT
Correlation Length
The distance over which events in a system are statistically connected — finite in subcritical systems, diverging to infinity at criticality, producing long-range correlations where perturbations anywhere affect configurations everywhere.
Correlation length measures how far influence propagates through a system — the spatial extent over which a perturbation at one point affects the behavior of other points. In subcritical systems, the correlation length is short: grains on opposite sides of a sandpile are independent, and events are local. As the system approaches criticality, the correlation length increases. At the critical point, it diverges — becomes infinite in principle, arbitrarily large in practice — meaning that the system becomes a single correlated domain where events at any location can influence events at any other location through chains of interaction. This divergence explains why systems at criticality exhibit long-range correlations, why avalanches can be system-wide, and why the AI transition feels simultaneous across the globe despite no central coordination.
In The You On AI Field Guide
The divergence of correlation length at criticality is one of the most mathematically rigorous predictions of critical phenomena theory. In a magnetic material approaching its Curie temperature, the correlation length