'Frustrated magnets'

bebis

1. The problem statement, all variables and given/known data

Consider three Ising spins located at the vertices of a triangular lattice, interacting antiferomagnetically with each other. The energy of an interacting spin pair is minimized when the spins are antiparaller. However, in this case, the energy cannot be minimized, since the third spin cannot be oriented.

According to which principle should the two spins be antiparaller, so that the energy is minimized?

2. Relevant equations

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3. The attempt at a solution

(1) Is it the principle of ‘minimum energy’ -that is applied everywhere?
(2) Is it the ‘Pauli exclusion principle’ valid here? We are not talking about spins of the same atom, but spins of three different atoms on a crystal though. But the ‘Pauli exclusion principle’ is valid for any two quantum systems that interact with each other. Isn’t it?
(3) The Hamiltonian that describes the magnetic interactions of the triangle is:
H=JΣ Si Sj. The energy of the system is minimized when: Stot=0.