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#### The J_{1}-J_{2} Model on the Anisotropic Triangular and the Square
Lattice: Similarities and Differences

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##### Citation

Schmidt, B., & Thalmeier, P. (2015). The J_{1}-J_{2} Model on the
Anisotropic Triangular and the Square Lattice: Similarities and Differences.* Acta Physica Polonica
A,* *127*(2), 324-326. doi:10.12693/APhysPolA.127.324.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0026-CA08-E

##### 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.