A Method of Determining the Ground State of the Extended Range Lattice Gas Model with Two Kinds of Particles

Abstract

An application of the method of geometrical inequalities to the rigorous determination of the ground state of the lattice gas model in which two kinds of particles interact by pairwise interactions of extended range is discussed. As an illustrative example we take the model on the one-dimensional lattice with first and second neighbor interactions, treating the whole region of particle densities, but imposing the condition that the k-th (k=1, 2) neighbor interaction constants between the same kinds of particles are equal and that the k-th (k=1, 2) neighbor interaction constant between different kinds of particles is half of those between the same kinds. It is found that seven types of ordered structures of particles appear as the ground states in this example.