Ground states of the lattice-gas model on the triangular lattice with nearest- and next-nearest-neighbor pairwise interactions and with three-particle interaction: Full-dimensional ground states

Abstract

In this paper, we completely solve the problem of the ground states 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. We use this model to illustrate how the complete solution of the ground-state problem of a lattice-gas model (or equivalent spin model) should look.