Ising-chain magnetization with spin-half normalization ($M/N=(g{\mu }_B/2)\sinh b/\sqrt{{\sinh }^{2}b+e^{-2\beta J}}$)

For $H=-2J\sum S_i^z{S}_{i+1}^z-g{\mu }_{B}B\sum S_i^z$, with dimensionless $S_i^z=\pm 1/2$, define $K=\beta J/2$ and $b=\beta g{\mu }_{B}B/2$. The transfer matrix for the one-dimensional Ising model has largest eigenvalue $e^K[\cosh b+\sqrt{{\sinh }^{2}b+e^{-4K}}]$. Differentiating its logarithm gives the displayed moment per site. In particular the zero-field susceptibility per site is $(g{\mu }_B{)}^2{e}^{\beta J}/(4k_{B}T)$. Factors of two differ from a model whose spin variables themselves take values $\pm 1$.