Molecule Formation and the Farey Tree in the One-Dimensional Falicov-Kimball Model

The ground state configurations of the one–dimensional Falicov–Kimball model are studied exactly with numerical calculations revealing unexpected effects for small interaction strength. In neutral systems we observe molecular formation, phase separation and changes in the conducting properties; while in non–neutral systems the phase diagram exhibits Farey tree order (Aubry sequence) and a devil’s staircase structure. Conjectures are presented for the boundary of the segregated domain and the general structure of the ground states.