08-22U

We propose a method for determination of the ground states of lattice gas (or Ising) models. The method permits 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 the third nearest neighbor interactions and we study the effect of the interactions up to the 19-th neighbors on this series. To our best knowledge, it is the second example of the devil's step at zero temperature in the lattice gas models with one kind of particles.