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.