English: Schematic equal-time spin correlation functions for ferromagnetic and antiferromagnetic materials both above and below their Curie temperatures versus the distance normalized by the correlation length, ${\displaystyle \xi }$. Note that in all cases, correlations are strongest nearest to the origin, indicating that a spin has the strongest influence on its nearest neighbors. Intuitively, all correlations gradually decay as the distance from the spin of interest increases. Note that above the Curie temperature, the correlation between spins tends to zero as the distance between the spins gets very large. This is in contrast to the case below the Curie temperature, where materials exhibit ordered spins. In such systems, 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. Intuitively, continuous order-disorder transitions can then be understood as process of the correlation length, ${\displaystyle \xi }$, transitioning from being infinite in a low-temperature, ordered state, to finite in a high-temperature, disordered state.