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 α. 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-α phase diagram is presented. A tricritical point is found in the spin-glass transition for Q>6, depending on α. Contrary to the Hopfield model, the critical lines do not converge to the same T as α→0. A stability analysis is made.