= Correlation function
{wiki}
A correlation function quantifies how measurements at different points or times vary together. For a scalar <order parameter>, the connected equal-time correlation is
$$
G(\mathbf r)=\langle\phi(\mathbf x+\mathbf r)\phi(\mathbf x)\rangle-\langle\phi(\mathbf x+\mathbf r)\rangle\langle\phi(\mathbf x)\rangle.
$$
The subtraction removes a contribution due solely to the mean values. Positive or negative values indicate enhanced alignment or anticorrelation relative to that independent baseline.
Its spatial decay defines a <correlation length>, while its <Fourier transform> gives the corresponding <static structure factor>. Scattering measurements therefore reveal collective structure through correlations even when individual microscopic configurations cannot be imaged. Equal-time, time-dependent and quantum time-ordered correlations are different objects; the measurement and operator ordering must identify which one is intended.
Back to article page
