  We study a coupled driven system in which two species of particles are
advected by a fluctuating potential energy landscape. While the particles
follow the potential gradient, each species affects the local shape of the
landscape in different ways. As a result of this two-way coupling between the
landscape and the particles, the system shows interesting new phases,
characterized by different sorts of long ranged order in the particles and in
the landscape. In all these ordered phases the two particle species phase
separate completely from each other, but the underlying landscape may either
show complete ordering, with macroscopic regions with distinct average slopes,
or may show coexistence of ordered and disordered regions, depending on the
differential nature of effect produced by the particle species on the
landscape. We discuss several aspects of static properties of these phases in
this paper, and we discuss the dynamics of these phases in the sequel.
