Correlation length
= Correlation length
{title2=$\xi$}
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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.