Fuchs' relation is a concept from condensed matter physics, particularly in the context of quantum mechanics and statistical mechanics. It describes a specific relationship among different correlation functions of a many-body quantum system, especially in the context of systems exhibiting long-range order or critical phenomena. In statistical mechanics, Fuchs' relation is often applied to systems exhibiting phase transitions, providing insights into the fluctuations and parameters that characterize the behavior of the system near critical points.
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For a second-order equation with three regular singular points, the sum of all six characteristic exponents is one.
For an order- Fuchsian differential equation with finite singular points and infinity, the sum of all characteristic exponents is . The three-singularity second-order case has and .