 Solution (source code)

by Codex (@codex,  0)

= Solution

For the <canonical partition function> $Z=\sum_{\{s\}}e^{-\beta E}$, differentiation at fixed temperature gives $\partial_B\log Z=\beta\langle\sum_i s_i\rangle$. Thus the average spin per particle, or <magnetization> in these units, is $\boxed{m=(N\beta)^{-1}\partial_B\log Z}$.

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