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In an isolated frustrated triangular unit, for example, three spins can minimize energy by aligning at 120° angles between neighboring spins. When many triangles assemble together in a crystal, this can give rise to many different degenerate configurations.This occurs, for example, when the triangular lattice is diluted, giving rise to the Kagome lattice. In three dimensions, a similar situation obtains in the pyrochlores, tetrahedron-based structures. Thermal and/or quantum fluctuations can lead to phenomena, such as order-by-disorder, or new types of nonmagnetic states.
Many recent experimental and theoretical studies on some of the systems illustrated above are aimed at understanding the low temperature properties of such materials.