Storage capacity of memory networks with binary couplings

We study the number p of unbiased random patterns which can be stored in a neural network of N neurons used as an associative memory, in the case where the synaptic efficacies are constrained to take the values ± 1. We find a solution with one step of replica symmetry breaking à la Parisi. This solution gives a critical capacity αc = p/N∼ 0.83 which seems to agree with known numerical results.