Infinite Series of Ground States of the Ising Model on the Honeycomb Lattice

Abstract

It is shown that the lattice gas version of the Ising model on the honeycomb lattice has infinite series of the regularly ordered ground states in the concentration range around the density x=1⁄2 when pairwise interactions satisfy the conditions given by V₁>4V₂−2V₃ and V₂>V₃≥0 or those by V₁>4V₂−3V₃, 2V₂>V₃, and V₃≤0 with V₁, V₂ and V₃ denoting the interaction constants of the first, second and third neighboring pairs, respectively; a positive interaction constant corresponds to a repulsive interaction. The equivalent Ising spin system has an infinite number of steps in the magnetization vs. field relation. Three kinds of infinite series of the ground states are found when the interaction constants are varied within the abovementioned conditions.