A Hopfield model with Hadamard prototypes

The properties of Hadamard matrices are used to construct suitable sets of prototype vectors for storage in Hopfield-like networks. Maximal sets ofp=N of such vectors are defined leading to sharp minima on the energy surface which act as attractors for the dynamics. A natural limit for such sets turns out to be <1/2. Dynamics are based on the flips of spinpairs of opposite sign, maintaining zero magnetization (zero bias) for all states under consideration. The flow to attractors in dynamics is discussed and the low-lying excitations from the ground states are calculated.