= Mean-field onset of two-state ferromagnetism
{title2=$m\sim\sqrt{3(1-T/T_C)}$}
For $m=\tanh(m/t)$ and positive temperature, the positive solution exists uniquely for $0<t<1$: the slope at zero is $1/t>1$, while the hyperbolic tangent is concave and below one. For $t\geq1$ only $m=0$ remains. Expanding to cubic order near $t=1$ gives $m^2\simeq3t^2(1-t)$ and $m\simeq t\sqrt{3(1-t)}$, with <mean-field critical exponent> $1/2$. The prefactor $t$ follows from the truncated equation; it is not controlled beyond leading critical order.
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