  We study numerically an inhomogeneous Ising lattice gas with short-range
interactions where different sectors are in contact with thermal baths at
different temperatures. Inside the different sectors particles jump to empty
sites following the familiar Kawasaki dynamics. In addition, particles can
freely hop from one sector to the other. This crossing between the sectors
breaks detailed balance and yields a local energy influx that drives the system
to a nonequilibrium steady state. When the low-temperature sector is cooled
below the equilibrium critical temperature, a complicated nonequilibrium phase
diagram emerges, dominated by unusual modulated nonequilibrium stationary
states. These steady states result from the interplay of phase separation and
convection.
