  Starting from the mutual information we present a method in order to find a
hamiltonian for a fully connected neural network model with an arbitrary,
finite number of neuron states, Q. For small initial correlations between the
neurons and the patterns it leads to optimal retrieval performance. For binary
neurons, Q=2, and biased patterns we recover the Hopfield model. For
three-state neurons, Q=3, we find back the recently introduced
Blume-Emery-Griffiths network hamiltonian. We derive its phase diagram and
compare it with those of related three-state models. We find that the retrieval
region is the largest.
