Thermodynamic properties of the<i>Q</i>-state Potts-glass neural network

Abstract

The Q-state Potts model of neural networks, extended to include biased patterns, is studied for extensive loading \ensuremath{\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-\ensuremath{\alpha} phase diagram is presented. A tricritical point is found in the spin-glass transition for Q&gt;6, depending on \ensuremath{\alpha}. Contrary to the Hopfield model, the critical lines do not converge to the same T as \ensuremath{\alpha}\ensuremath{\rightarrow}0. A stability analysis is made.