Gardner optimal capacity of the diluted Blume-Emery-Griffiths neural network

The optimal capacity of a diluted Blume-Emery-Griffiths neural network is studied as a function of the pattern activity and the embedding stability using the Gardner entropy approach. Annealed dilution is considered, cutting some of the couplings referring to the ternary patterns themselves and some of the couplings related to the active patterns, both simultaneously (synchronous dilution) or independently (asynchronous dilution). Through the de Almeida-Thouless criterion it is found that the replica-symmetric solution is locally unstable as soon as there is dilution. The distribution of the couplings shows the typical gap with a width depending on the amount of dilution, but this gap persists even in cases where a particular type of coupling plays no role in the learning process.