Correlation function (statistical mechanics): Difference between revisions

Revision as of 22:32, 12 June 2023

Revision as of 23:02, 14 June 2023

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===Magnetism===

In a [[Spin (particle physics)|spin]] system, the equal-time correlation function is especially well-studied. It describes the canonical ensemble (thermal) average of the scalar product of the spins at two lattice points over all possible orderings:

<math>C (r) = \langle \mathbf{s}(R) \cdot \mathbf{s}(R+r)\rangle\ - \langle \mathbf{s}(R) \rangle\langle \mathbf{s}(R+r) \rangle\,.</math>

Here the brackets mean the above-mentioned thermal average. Schematic plots of this function are shown for a ferromagnetic material below, at, and above its Curie temperature on the left.