  In most studies of the channel capacity of quantum channels, it is assumed
that the errors in each use of the channel are independent. However, recent
work has begun to investigate the effects of memory or correlations in the
error. This work has led to speculation that interesting non-analytic behaviour
may occur in the capacity. Motivated by these observations, we connect the
study of channel capacities under correlated error to the study of critical
behaviour in many-body physics. This connection enables us the techniques of
many-body physics to either completely solve or understand qualitatively a
number of interesting models of correlated error. The models can display
analogous behaviour to associated many-body systems, including `phase
transitions'.
