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We numerically investigate an S=1/2 spin model, in which two dimerized antiferromagnetic rings interact with each other ferromagnetically. It is shown that the order of the magnetoelastic transition is strongly affected by the interring coupling J<Subscript>⊥</Subscript> and there may exist a critical J<Subscript>⊥</Subscript> <Superscript>*</Superscript>...</superscript></subscript></subscript>
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