For the arbitrary forces the extension-force dependence will be given by Langevin function:
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The spring force law is governed by inverse Langevin function or approximated by the Warner's relationship
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The Brillouin function is then simplified into the "'Langevin function "', named after Paul Langevin:
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In the case of isotropic magnetic materials, Boltzmann distribution can be reduced to Langevin function connecting isotropic anhysteretic magnetization with effective magnetic field H _ \ text { e }:
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