  We study the stable phases of an attractor neural network model, with binary
units, for hippocampal place cells encoding 1D or 2D spatial maps or
environments. Using statistical mechanics tools we show that, below critical
values for the noise in the neural response and for the number of environments,
the network activity is spatially localized in one environment. We calculate
the number of stored environments. For high noise and loads the network
activity extends over space, either uniformly or with spatial heterogeneities
due to the cross-talk between the maps, and memory of environments is lost.
Analytical predictions are corroborated by numerical simulations.
