Abstract
A one-dimensional antiferromagnetic Ising chain with spin-lattice coupling is considered. If the underlying lattice is harmonic but has no translational symmetry, there appears at zero temperature an effective interaction between down spins, which is repulsive and decays exponentially with distance. It is shown rigorotusly that this system exhibits in the ground state a devil's staircase as a function of an external magnetic field on account of the effective long range interaction. The ground state phase diagram is also given.
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