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An exotic example of itinerant-electron magnetism is the so-called "flat-band ferromagnetism" arising in a wide class of geometrically frustrated lattices. Here electrons become trapped in restricted parts of the lattice and may favor a ferromagnetic state at a certain electronic filling.
An early remark linked this problem to one of percolation where appearance of a large cluster of trapped electrons is equivalent to the onset of ferromagnetism in a system. We found that due to the Pauli-principle ferromagnetic electronic clusters interact via an unusual repulsive quantum-statistical interaction. This interaction gives rise to an entirely novel "Pauli-correlated" percolation problem. In contrast to standard percolation, its percolation transition is of the first order and leads to the coexistence of ferromagnetic and paramagnetic phases in a wide region of electronic concentrations for dimensions D>=2 [1]. The PCP problem is an unusual statistical physics problem on its own right. We provide an exact solutions for it in 1D chain and the Bethe lattice [2]. [1] M. Maksymenko, A. Honecker, R. Moessner, J. Richter, and O. Derzhko, Phys. Rev. Lett. 109, 096404 (2012) [2] M. Maksymenko, K. Shtengel, R. Moessner, in preparation |
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