  The phenomenon of phase transitions in one-dimensional systems is discussed.
Equilibrium systems are reviewed and some properties of an energy function
which may allow phase transitions and phase ordering in one dimension are
identified. We then give an overview of the one-dimensional phase transitions
which we have been studied in nonequilibrium systems. A particularly simple
model, the zero-range process, for which the steady state is know exactly as a
product measure, is discussed in some detail. Generalisations of the model, for
which a product measure still holds, are also discussed. We analyse in detail a
condensation phase transition in the model and show how conditions under which
it may occur may be related to the existence of an effective long-range energy
function. Although the zero-range process is not well known within the physics
community, several nonequilibrium models have been proposed that are examples
of a zero-range process, or closely related to it, and we review these
applications here.
