Magnetoelastic instability in the XXZ rings with next-nearest neighbour coupling

This paper numerically investigates the magnetoelastic instability in the S = 1/2 XXZ rings containing finite spins N with antiferromagnetic nearest-neighbour (NN) and next-nearest neighbour (NNN) coupling. It finds that, as the NNanisotropy \varDelta_1 equals the NNN anisotropy \varDelta_2, there exists a critical NNN coupling strength J_2^\rm c (≈0.5), at which the systems always locate in dimerized phase for arbitrary large spring constant. As \varDelta_1\neq\varDelta_2, the values of J_2^\rm c are dependent on N and the difference of (\varDelta_1-\varDelta_2).