= Ising-chain magnetization with spin-half normalization
{c}
{title2=$M/N=(g\mu_B/2)\sinh b/\sqrt{\sinh^2b+e^{-2\beta J}}$}
For $H=-2J\sum S_i^zS_{i+1}^z-g\mu_BB\sum S_i^z$, with dimensionless $S_i^z=\pm1/2$, define $K=\beta J/2$ and $b=\beta g\mu_BB/2$. The <transfer matrix for the one-dimensional Ising model> has largest eigenvalue $e^K[\cosh b+\sqrt{\sinh^2b+e^{-4K}}]$. Differentiating its logarithm gives the displayed moment per site. In particular the zero-field susceptibility per site is $(g\mu_B)^2e^{\beta J}/(4k_BT)$. Factors of two differ from a model whose spin variables themselves take values $\pm1$.
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