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

We derive a universal form for the correlation function of general n-component systems in the limit of high temperatures or weak coupling. This enables the extraction of effective microscopic interactions from measured high-temperature correlation functions. We find that in systems with long-range interactions, there exist diverging correlation lengths with amplitudes that tend to zero in the high-temperature limit. For general systems with disparate long-range interactions, we introduce the notion of generalized Debye length (and time) scales and further relate these to the divergence of the largest correlation length in the high-temperature (or weak-coupling) limit.