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Replace the applied field in the doublet response by the Weiss molecular field $B_E={\mu }_0\lambda M$. At zero applied field,The equation is odd in $M$, so the two ordered orientations have equal magnitude. With $m=|M|/(n{\mu }_B)$, defineThe mean-field self-consistency equation becomesPlot $y=m$ and $y=\tanh (m/t)$. The second has slope $1/t$ at zero and is concave for positive $m$. For $0<t<1$ it starts above the straight line but is below it by $m=1$, giving one positive intersection. For $t\ge 1$, $\tanh (m/t)<m$ for every $m>0$. HenceAt $T=0$ the limiting solution is $m=1$. The onset of spontaneous magnetization is the mean-field Curie temperature.

The Weiss molecular field replaces exchange coupling to neighbouring moments by an effective local field proportional to the average magnetization. For two-state moments and $B_E={\mu }_0\lambda M$, self-consistency gives $m=\tanh (m/t)$ at zero applied field, where $m=|M|/(n\mu )$ and $t=T/T_C$, with $k_B{T}_C={\mu }_0\lambda n{\mu }^2$. This field represents a quantum exchange energy, not generally the actual magnetostatic field generated by the moments.