In considering next-nearest neighbor (NNN) coupling, we numerically investigate the magnetoelastic instabilityin ring-shaped mesoscopic antiferromagnetic Heisenberg spin 1/2 systems with spin-phonon interaction. Theresults indicate that, for antiferromagnetic NNN coupling J_2,there may be a critical value J_2~c, at which the ground stateis dimerized for arbitrary lattice spring constant and beyond and below which the magnetoelastic instability behavioris different from each other. The values of J_2~c are irrelevant to the system size. For ferromagnetic NNN coupling, onlycontinuous transition is present from dimerized phase to uniform phase as lattice spring constant is increased.
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