The storage capacity of the Blume-Emery-Griffiths neural network

We analyse the so-called Blume-Emery-Griffiths (BEG) neural network at zero temperature. An upper bound on its storage capacity is given if we want the stored patterns to be fixed points of the retrieval dynamics. Besides, we discuss a more liberal notion of storage capacity introduced by Newman (1988 Neural Netw. 1223-38) in the context of the Hopfield model (Hopfield 1982 Proc. Natl Acad. Sci. USA 79 2554-8). We show that, similar to the findings in the neural networks literature, the BEG model with this notion of storage capacity can store a number of patterns proportional to the number of neurons in the model.