  The dynamical organization in the presence of noise of a Boolean neural
network with random connections is analyzed. For low levels of noise, the
system reaches a stationary state in which the majority of its elements acquire
the same value. It is shown that, under very general conditions, there exists a
critical value of the noise, below which the network remains organized and
above which it behaves randomly. The existence and nature of the phase
transition are computed analytically, showing that the critical exponent is
1/2. The dependence of the critical noise on the parameters of the network is
obtained. These results are then compared with two numerical realizations of
the network.
