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Abstract:
The Heisenberg model on a triangular lattice is a prime example for a
geometrically frustrated spin system. However most experimentally
accessible compounds have spatially anisotropic exchange interactions.
As a function of this anisotropy, ground states with different magnetic
properties can be realized. On the other hand, the J(1)-J(2) model on
the square lattice is a well-known example for frustration induced by
competing exchange. The classical phase diagrams of the two models are
related in a broad range of the control parameter phi -
tan(-1)(J(2)/J(1)). In both cases three different types of ground states
are realized, each model having a ferromagnetic and an antiferromagnetic
region in the phase diagram, and a third phase with columnar magnetic
order for the square lattice and an in general incommensurate spiral
structure for the triangular lattice. Quantum effects lift degeneracies
in the non-FM phases and lead to additional nonmagnetic regions in the
phase diagrams. The contribution of zero point fluctuations to ground
state energy, wave vector, and ordered moment is discussed.
