Antiferromagnetic Ising ring
= Antiferromagnetic Ising ring
{title2=$H=J\sum_{j=1}^NS_jS_{j+1},\quad J>0,\quad S_{N+1}=S_1$}
An <antiferromagnetic Ising model> on a closed one-dimensional ring, with <Ising spins> $S_j=\pm1$ and the displayed <periodic boundary conditions>. Every opposite neighboring pair minimizes its bond <energy>. An even ring admits two completely alternating <ground states>; an odd ring must contain at least one parallel pair, an example of <geometric frustration>.