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# Correlation function (statistical mechanics)

The correlation function in statistical mechanics is measure of the order in a system. It tells us how microscopic variables at different positions are correlated. In a spin system, it is the thermal average of the scalar product of the spins at two lattice points over all possible orderings. The correlation function is hence,

$G (r) = \langle \mathbf{s}(R) \cdot \mathbf{s}(R+r)\rangle_{\mbox{Thermal average}}$

$G (r) = \frac{1}{r^{d-2+\eta}}\exp{\left(\frac{-r}{\xi}\right)}$