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We investigate a detail of a dodecamer cluster ordering in a double-exchangespin ice model on a kagom\'e lattice. In frustrated systems, ordinary spinorderings are suppressed and macroscopic degeneracy remains down to lowtemperatures. In some frustrated systems, the degeneracy is lifted due toresidual interactions and cluster orderings are stabilized. In the presentmodel, the spin ice state is first formed at intermediate temperatures, andfurther entropies are released at lower temperatures as the dodecamer phaseemerges. Since the spin symmetry is not broken in the dodecamer phase, therestill exists macroscopic degeneracy. At further low temperatures, a possiblespin ordering due to inter-dodecamer interactions is proposed. We discuss thatsuch a multiple-site clustering larger than a bond-pair might be generic tofrustrated systems where macroscopic degeneracy is lifted by residualinteractions.Comment: 18 pages, 11 figure

Frustration-induced Dodecamer Ordering in the Double-Exchange Spin Ice Model on the Kagomé Lattice