= Vanishing disordered-side heat-capacity amplitude in Landau theory
{title2=$C_{\mathrm{sing},+}=0$}
For $F=F_{\mathrm{reg}}+am^2/2+cm^6/6$, $c>0$, $a=a_0(T-T_c)$, the ordered <global minimum> gives $F-F_{\mathrm{reg}}=-(-a)^{3/2}/(3\sqrt c)$ and $C_{\mathrm{sing},-}=Ta_0^2/(4\sqrt c\sqrt{-a})$. On the disordered side the minimum is exactly $m=0$, so the polynomial's <heat capacity> is zero. The tricritical scaling label $\alpha=1/2$ can be used with zero upper-side amplitude, but no nonzero upper-side power law follows from this saddle alone. A smooth background such as $F_{\mathrm{reg}}=-C_0T\log(T/T_*)$ gives a finite upper-side <heat capacity> $C_0$ without changing the <phase diagram>.
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