  A driven system of three species of particle diffusing on a ring is studied
in detail. The dynamics is local and conserves the three densities. A simple
argument suggesting that the model should phase separate and break the
translational symmetry is given. We show that for the special case where the
three densities are equal the model obeys detailed balance and the steady-state
distribution is governed by a Hamiltonian with asymmetric long-range
interactions. This provides an explicit demonstration of a simple mechanism for
breaking of ergodicity in one dimension. The steady state of finite-size
systems is studied using a generalized matrix product ansatz. The coarsening
process leading to phase separation is studied numerically and in a mean-field
model. The system exhibits slow dynamics due to trapping in metastable states
whose number is exponentially large in the system size. The typical domain size
is shown to grow logarithmically in time. Generalizations to a larger number of
species are discussed.
