Mean field models and inverse problem

The inverse problem is tested for a class of statistical mechanics mean-field models: the Curie-Weiss model together with its multi-species version and the monomer-dimer model with attractive interaction. In particular, we show that the inversion is obtained by analytically identifying the model parameters in terms of the correlation functions. Moreover, we show that the robustness of the inversion procedure depends on the knowledge of the phase space of the system.