= Magnetization scaling-function matching
{title2=$m=|t|^{2-\alpha-\Delta}g_{m,\pm}(h/|t|^\Delta)$}
Differentiate $f_s=|t|^{2-\alpha}g_{f,\pm}(h/|t|^\Delta)$ with respect to its <conjugate field>. A finite nonzero one-sided ordered-branch <amplitude> gives $\beta=2-\alpha-\Delta$. To approach a finite critical isotherm as $t\to0$ at fixed small $h$, the large-argument function must behave as $g_m(x)\sim C\operatorname{sgn}(x)|x|^{1/\delta}$. Cancelling the remaining thermal power yields $\beta=\Delta/\delta$. An analytic background, branch selection and <thermodynamic limit> must be distinguished from the singular <free energy> being differentiated.
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