Ground states of the lattice-gas model on the triangular lattice with nearest- and next-nearest-neighbor pairwise interactions and with three-particle interaction: ground states at boundaries of full-dimensional regions.

We analyze the ground states at boundaries of four-dimensional (full-dimensional) ground-state regions of the lattice-gas model on the infinite plane triangular lattice with nearest- and next-nearest-neighbor pairwise interactions and with additional interaction between three particles at the vertices of a nearest-neighbor triangle. In such a way we determine the ground states at fixed density of particles (coverage) and make the comparison to experiments possible. A surprisingly rich variety of structures is found: ordered periodic, ordered-but-aperiodic, disordered with various degree of disorder, and multiple-twin structures. The first-order and continuous phase transitions are identified. The degree of disorder for disordered ground states is analyzed. One of the most interesting results is the discovery of an infinite sequence of ground states at a boundary between two phases.