  We construct for the first time examples of non-frustrated, two-body,
infinite-range, one-dimensional classical lattice-gas models without periodic
ground-state configurations. Ground-state configurations of our models are
Sturmian sequences defined by irrational rotations on the circle. We present
minimal sets of forbidden patterns which define Sturmian sequences in a unique
way. Our interactions assign positive energies to forbidden patterns and are
equal to zero otherwise. We illustrate our construction by the well-known
example of the Fibonacci sequences.
