  We study a family of diluted attractor neural networks with a finite average
number of (symmetric) connections per neuron. As in finite connectivity spin
glasses, their equilibrium properties are described by order parameter
functions, for which we derive an integral equation in replica symmetric (RS)
approximation. A bifurcation analysis of this equation reveals the locations of
the paramagnetic to recall and paramagnetic to spin-glass transition lines in
the phase diagram. The line separating the retrieval phase from the spin-glass
phase is calculated at zero temperature. All phase transitions are found to be
continuous.
