= Ising-chain domain-wall energy convention
{c}
{title2=$\Delta E_{\rm wall}=J\quad\text{for }H=-2J\sum S_i^zS_{i+1}^z$}
For $J>0$ and $S_i^z=\pm1/2$, 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 $-J\sum s_is_{i+1}$ 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 $ae^{\beta J}/2$.
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