  The short-range attraction and long-range repulsion (SALR) between
nanoparticles or macromolecules can lead to spontaneous pattern formation on
solid surfaces, fluid interfaces or membranes. In order to study the
self-assembly in such systems we consider a triangular lattice model with
nearest-neighbour attraction and third-neighbour repulsion. At the ground state
of the model ($T=0$) the lattice is empty for small values of the chemical
potential $\mu$, and fully occupied for large $\mu$. For intermediate values of
$\mu$ periodically distributed clusters, bubbles or stripes appear if the
repulsion is sufficiently strong. At the phase coexistences between the vacuum
and the ordered cluster phases and between the cluster and the lamellar
(stripe) phases the entropy per site does not vanish. As a consequence of this
ground state degeneracy, disordered fluid phases consisting of clusters or
stripes are stable, and the surface tension vanishes. For $T>0$ we construct
the phase diagram in the mean-field approximation and calculate the correlation
function in the self-consistent Brazovskii-type field theory.
