Magnetoelastic instability in Ising-like models

The magnetoelastic instability in nanostructured ring-shaped Ising-like spin 1/2 model has been investigated by using the exact diagonalization method. It is found that there exists two critical anisotropy parameters Δc(1) and Δc(2) (Δc(1)<Δc(2)) in the phase diagram. As the anisotropy parameter Δ>Δc(2), the magnetoelastic transition from dimerized phase to uniform phase is a first order transition with an increase of the lattice spring constant. While for Δ<Δc(2), the transition is continuous. Another critical value Δc(1) divides the different lattice distortion behavior as the anisotropy is strengthened.