= Zero-temperature correlation of an odd antiferromagnetic Ising ring
{title2=$C_n=(-1)^n(1-2n/N)$}
At fixed odd $N$, the zero-<temperature> <canonical ensemble> equally weights the $2N$ <ground states> of an <antiferromagnetic Ising ring>. The single <frustrated bond in an antiferromagnetic Ising ring> lies on a chosen $n$-bond path with <probability> $n/N$. The <Ising spin> product is $(-1)^n$ if the path excludes that bond and $-(-1)^n$ if it includes it, proving the displayed <two-point correlation function>. The loss of staggered alignment upon averaging persists at zero <temperature> and is caused by <geometric frustration>, rather than a positive density of thermal defects. The expression remains symmetric under $n\mapsto N-n$ for odd $N$.
Back to article page
