A Devil's Staircase and the Ground State Phase Diagram in an Ising Chain with Spin-Lattice Coupling

Abstract

A one-dimensional Ising chain with spin-lattice coupling is considered. If the lattice is harmonic but has no translational symmetry, there appears effectively through the spin-lattice coupling a four-spin interaction which decays exponentially with distance. It is shown rigorously that this spin system in the ground state exhibits a devil's staircase as a function of the exchange parameter J because of the long range interaction. The ground state phase diagram of the spin system under an external magnetic field is speculated.