Ground states of lattice-gas models on the triangular and honeycomb lattices: Devil's step and quasicrystals

We propose a method for determining the ground states of lattice-gas (or Ising) models. The method makes possible to find all types of ground states, including chaotic and ordered-but-aperiodic ones, and to identify the first-order phase transitions between them. Using this method, we prove the existence of an infinite series of ground states (the so-called devil's step) in the lattice-gas model on the triangular lattice with up to third nearest-neighbor interactions and we study the effect of the interactions up to 19th neighbors on this series. To our best knowledge, this is only the second example of the devil's step at zero temperature in the lattice-gas models with one kind of particles.