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 {NN} anisotropy Δ₁ equals the {NNN} anisotropy \varDelta₂, there exists a critical {NNN} coupling strength J₂^c(≈0.5), at which the systems always locate in dimerized phase for arbitrary large spring constant. As Δ₁ \ne Δ₂, the values of J₂^{\rm c} are dependent on N and the difference of (Δ₁-\varDelta₂).