Mechanism for lifting the degeneracy in the double-exchange spin ice model on a kagom\'e lattice: Dodecamer formation

We investigated the double-exchange spin ice model on a kagom\'e lattice by Monte Carlo simulation in order to study a mechanism for lifting the degeneracy in frustrated electron systems. We show specific heat and vector spin chirality data on a finite lattice. Specific heat has a double-peak structure: A broad peak and a sharp peak are at $k_{\rm B}T/t \sim 0.15$ and 0.015, respectively, where $t$ is the transfer integral of electrons. The broad peak corresponds to a crossover to the spin ice-like state, on the other hand, the sharp one a transition to a dodecagonal spin cluster (dodecamer) state. We discuss the interplay between the formation of the dodecamer state and the lifting of the macroscopic degeneracy.