= Curie–Weiss model
{c}
{title2=$\mathbb P(s)=Z_{n,\beta}^{-1}e^{\beta(\sum_i s_i)^2/(2n)}$}
The zero-field ferromagnetic Curie–Weiss model is an <Ising model> on $n$ spins with an equal interaction between every pair. For $s_i\in\{-1,1\}$ and $\beta>0$, its normalized <probability mass function> is $Z_{n,\beta}^{-1}\exp[\beta(\sum_is_i)^2/(2n)]$. The <partition function> $Z_{n,\beta}$ sums these weights over all configurations. The square includes constant diagonal terms; these affect only normalization. <Spin inversion symmetry> makes every spin's <expected value> zero, while grouping configurations by their <spin magnetization> gives
$$
\mathbb P(M=m)=Z_{n,\beta}^{-1}\binom{n}{n(1+m)/2}e^{\beta nm^2/2}.
$$
Here $m=-1+2k/n$, $0\leq k\leq n$.
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