= Classical Heisenberg Langevin self-consistency
{title2=$S=\coth(\beta z_cJS)-1/(\beta z_cJS)$}
The single-site average in molecular field $z_cJS$ is $S=\coth x-1/x$, where $x=\beta z_cJS$. Thus $\tau x=\coth x-1/x$ with $\tau=k_BT/(z_cJ)$. The small-$x$ slope $1/3$ gives $k_BT_c^{\rm MF}=z_cJ/3$. On a <square lattice> $z_c=4$. This finite mean-field transition does not imply actual positive-temperature <magnetization> for the ideal two-dimensional short-range isotropic model, where the <Mermin-Wagner theorem> applies.
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