Correlation function

Summary

A correlation function of a statistical system measures how the values of a local quantity at several points depend on each other. The basic one is the truncated two-point function $\langle \sigma_x \sigma_y \rangle - \langle \sigma_x \rangle \langle \sigma_y \rangle$ of a spin system. Its rate of decay with the distance $\abs{x - y}$ defines the correlation length. Away from a critical point it typically decays exponentially. At a critical point it decays like a power, and the power gives a critical exponent.