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The ground state configurations of the one--dimensional Falicov--Kimballmodel are studied exactly with numerical calculations revealing unexpectedeffects for small interaction strength. In neutral systems we observe molecularformation, phase separation and changes in the conducting properties; while innon--neutral systems the phase diagram exhibits Farey tree order (Aubrysequence) and a devil's staircase structure. Conjectures are presented for theboundary of the segregated domain and the general structure of the groundstates.Comment: LaTeX file, 38 pages, postscript figures (not included) are available  by reques

Molecule formation and the Farey tree in the one-dimensional Falicov-Kimball model