standard deviations over 10 subnetworks for each $N$ and $\alpha$.\[alpha\_fig\]](fig5){width="\linewidth"}

At $\alpha=0$, the model describes a population of independent neurons, so that the distribution of correlation coefficients across the populations consists of a singular peak at $C=0$ (Fig \[alpha\_fig\]A, left panel). As $\alpha$ is increased beyond the strength of correlations present in the data ($\alpha=1$, Fig \[alpha\_fig\]A, middle panel), the distribution of correlations broadens such that at $\alpha=2$ some pairs are very strongly correlated (Fig \[alpha\_fig\]A, right panel). This is reflected in a distribution of frequent joint activity states that seem to cluster around a small number of prototypical patterns, much as in the Hopfield model of associative memories [@hopfield_82; @amit_89]. The entropy vs energy plot for the corresponding network, shown in Fig 5B, singles out the ensemble at $\alpha=1$ as the one whose density of states aligns most closely with the diagonal: going towards independence (smaller $\alpha$) gives rise to a concave bump at low energies, while $\alpha>1$ ensembles deviate away from the equality line more at high energies. Interestingly, the drop in entropy from independence to $\alpha=1$ is modest, consistent with our previous reports [@tkacik+al_14a], and the entropy decreases substantially only at high $\alpha$ and large $N$, as 