= Exchange interaction
{wiki}
The <exchange interaction> is an effective interaction between <spins> originating in the quantum mechanics of <Electrons>. Its sign convention must accompany any formula. For the illustrative classical fixed-length <spin> pair used here, write
$$
E=J\mathbf S_1\cdot\mathbf S_2=JS^2\cos\theta.
$$
With this plus-sign convention, $J>0$ favors antiparallel <spins>: $E(\pi)=-JS^2$, compared with $E(0)=+JS^2$. The <energy> difference is $2JS^2$. If instead the <Hamiltonian> is written with an overall minus sign, the same physical preference has a negative coupling. This prevents a sign convention in the <Ising model> from being mistaken for a disagreement about the ordering.
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