Non - Degenerate Ground State in the Antiferromagnetic Double - Exchange Model on a Triangular Lattice

In order to study effects of frustration in an itinerant electron system, we investigate ground states of the antiferromagnetic double-exchange model on a triangular lattice. In this model, pseudo-spins are coupled to electron transfer integrals in such a way that antiparallel configurations of pseudo-spins gain kinetic energies. Although the antiferromagnetic Ising model on a triangular lattice shows macroscopic dengenerate ground states, the present model shows that the degeneracy is lifted due to long-range natures of the double exchange interactions. Spin ordering at the ground state is also discussed.