It is known that Matthiessen's rule is valid only when we consider different scattering processes as independent. However, when there is correlation between these scattering processes, this rule is not applicable anymore. What i am trying to figure out is, do we have any analog of the Matthiessen's rule violation for magnetization (or susceptibility)?
The Matthiessen rule is never strictly valid; it is only valid in some asymptotic sense, as in the case of the electron-phonon problem in the adiabatic limit where √(m/M) → 0, with m the effective mass of the electrons and M the mass of the lightest isotope of the constituent atoms. This can be appreciated by considering the perturbation expansion of whatever correlation function one has in mind in terms of more than one coupling constant of interaction. To be explicit, consider a case involving two coupling constants of interaction, λ1 and λ2. Consistency requires that in the n-th order of the perturbation theory one takes account of all perturbative contributions proportional to λ1l+ λ2m with l+m=n. Only in the case of n = 1 has one (l,m) = (1,0) and (0,1), corresponding to strictly additive contributions. For n > 1, one has also mixing contributions (as in the case of n=2, where one has also (l,m) = (1,1)), the latter leading to the violation of the Matthiessen rule. The above-mentioned asymptotic sense (as in the case of √(m/M) → 0) corresponds to the situations where either λ1/λ2 → 0 or λ2/λ1 → 0.
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