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In this work we compare two different random dilution of a mean fieldferromagnet: the first model is built on a Bernoulli-diluted network while thesecond lives on a Poisson-diluted network. While it is known that the twomodels have in the thermodynamic limit the same free energy we investigate onthe structural constraints that the two models must fulfill. We rigorouslyderive for each model the set of identities for the multi-overlaps distributionusing different methods for the two dilutions: constraints in the former modelare obtained by studying the consequences of the self-averaging of the internalenergy density, while in the latter are obtained by a stochastic-stabilitytechnique. Finally we prove that the identities emerging in the two models arethe same, showing "robustness" of the ferromagnetic properties of dilutednetworks with respect to the details of dilution.

Dilution Robustness for Mean Field Ferromagnets