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 it to the divergence of the largest correlation length in the high temperature (or weak coupling) limit.

💡 Research Summary

The paper presents a unified theoretical framework for the two‑point correlation function of generic n‑component spin‑like systems in the high‑temperature (or weak‑coupling) limit. Starting from a Hamiltonian that includes arbitrary pairwise exchange interactions V(x‑y) and an external field, the authors perform a Hubbard‑Stratonovich transformation to introduce an auxiliary field η(x). In the β→0 regime the η‑field becomes Gaussian, allowing an exact evaluation of the correlation function. The resulting universal expression,

 G(k)=⟨|S(k)|²⟩ = k_B T /