The J₁-J₂ Model on the Anisotropic Triangular and the Square Lattice: Similarities and Differences

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