 Ising-chain domain-wall energy convention

For $J>0$ and $S_i^z=\pm 1/2$, a parallel bond has energy $-J/2$ while an antiparallel bond has $+J/2$. A wall therefore costs J, rather than the $2J$ of a differently normalized $-J\sum s_i{s}_{i+1}$ model. At zero field its density is $[1-\tanh (\beta J/2)]/2$, positive at every nonzero temperature. Walls occur in pairs on a periodic ring, but that global parity restriction does not remove their nonzero density in the thermodynamic limit. The low-temperature correlation length is approximately $a{e}^{\beta J}/2$.