THERMODYNAMIC PROPERTIES OF THE Q-STATE POTTS-GLASS NEURAL NETWORK

The Q-state Potts model of neural networks, extended to include biased patterns, is studied for extensive loading alpha. Within the replica-symmetric approximation, mean-field equations are written down for general Q and arbitrary temperature T. The critical storage capacity is discussed for Q = 3 and two classes of representative bias parameters. The complete T-alpha phase diagram is presented. A tricritical point is found in the spin-glass transition for Q > 6, depending on alpha. Contrary to the Hopfield model, the critical lines do not converge to the same T as alpha --> 0. A stability analysis is made.