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We derive a universal form for the correlation function of general ncomponent systems in the limit of high temperatures or weak coupling. Thisenables the extraction of effective microscopic interactions from measured hightemperature correlation functions. We find that in systems with long rangeinteractions, there exist diverging correlation lengths with amplitudes thattend to zero in the high temperature limit. For general systems with disparatelong range interactions, we introduce the notion of generalized Debye length(and time) scales and further relate it to the divergence of the largestcorrelation length in the high temperature (or weak coupling) limit.

physical review. b, condensed matter and materials physics

High temperature correlation functions: universality, extraction of  exchange interactions, divergent correlation lengths and generalized Debye  length scales