Thermodynamics of fully connected Blume-Emery-Griffiths neural networks

The thermodynamic and retrieval properties of fully connected Blume-Emery-Griffiths networks are studied using replica mean-field theory. These networks can be considered as generalizations of the Hopfield model to the storage of ternary patterns. Capacity-temperature phase diagrams are derived for several values of the pattern activity. It is found that the retrieval phase is the largest in comparison with other three-state neuron models. Furthermore, the meaning and stability of the so-called quadrupolar phase is discussed as a function of both the temperature and the pattern activity. Where appropriate, the results are compared with the diluted version of the model.