Ising models for networks of real neurons

Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the retina, and show that pairwise interactions account for observed higher-order correlations. By first finding a representative ensemble for observed networks we can create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical point and start exhibiting collective behaviors reminiscent of spin glasses.