Can Geometrical Frustration be Relieved in Heisenberg Spins?

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The discussion centers on the concept of geometrical frustration in magnetism, specifically regarding Heisenberg spins and Ising spins on a triangular lattice. It concludes definitively that the frustration cannot be relieved for Heisenberg spins without altering the lattice structure or introducing interactions with second or third neighbors. Distorting the lattice or modifying coupling parameters are necessary actions to address this frustration.

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In magnetism, the antiferromagnetic interaction between ising spin on a regular triangle is the simplest example of geometrical frustration. Is it possible that this frustration relieved for Heisenberg spins??
 
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No. Even for Heisenberg spins the lattice is still frustrated.

In order to remove the frustration you have to distort the lattice (i.e. introduce a difference in the coupling paramters) or introduce interactions with second or third neighbors (can't remember the details, sorry).
 

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