We simulate each network for 105 steps for different values of β, and we find that all the heat capacity of the 10 networks diverges at the operating temperature β = 1 (Fig. 2A), showing values similar to those of the original lattice Ising model with periodic boundaries. Let us point out that although the distribution of correlations is similar to the lattice Ising model, the structure of the network is radically changed. Instead of the original ordered structure of a uniform lattice, we now have a disordered distribution of couplings Jij (Fig. 2B), including both positive and negative values. Also, each execution of the learning algorithm yields a completely different arrangement of values of couplings Jij.Figure 2(A) Divergence of the heat capacity in 10 models after learning random correlations sampled from Fig. 1. Maximum and minimum values are shown by the grey area. (B) Distribution of the values of the coupling matrix Jij of a 64 units Ising model after learning correlations sampled from Fig. 1. (the order of the nodes in the coupling matrix has been arranged using hierarchical clustering). Values of Jij correspond to the values in the colour bar.