File:Magnetic moments as a function of position in ferro and antiferromagets.svg

English: Schematic equal-time spin correlation functions for ferromagnetic and antiferromagnetic materials both above and below ${\displaystyle T_{Curie}}$ versus the distance normalized by the correlation length, ${\displaystyle \xi }$. In all cases, correlations are strongest nearest to the origin, indicating that a spin has the strongest influence on its nearest neighbors. All correlations gradually decay as the distance from the spin at the origin increases. Above the Curie temperature, the correlation between spins tends to zero as the distance between the spins gets very large. In contrast, below ${\displaystyle T_{Curie}}$, the correlation between the spins does not tend toward zero at large distances, but instead decays to a level consistent with the long-range order of the system. The difference in these decay behaviors, where correlations between microscopic random variables become zero versus non-zero at large distances, is one way of defining short- versus long-range order.