 Correlation length

The correlation length is a characteristic distance over which connected spatial fluctuations remain correlated. Away from a critical point, a common large-distance form is $G(r)\sim r^{-p}{e}^{-r/\xi }$; the exponential decay scale $\xi$ is one standard definition. Other definitions, such as a second-moment length, can differ by finite factors.

Near an ordinary continuous phase transition, $\xi$ grows as $|t{|}^{-\nu }$. In scattering, a larger correlation length produces a narrower feature around the ordering wavevector: a Gaussian kernel $A+\kappa q^2$ gives a width of order $1/\xi$ with $\xi =\sqrt{\kappa /A}$. Finite system size cuts off this growth. A correlation length measures collective organization rather than the size of an individual atom, molecule or magnetic moment.