= Large-quartic asymptotic of tricritical scaling
{title2=$\Phi_-(X,0)\sim-1/(4X)$}
On the ordered branch of <tricritical crossover scaling>, at zero field and $X\to+\infty$, the minimizing square is $a=\psi^2=(\sqrt{X^2+4}-X)/2\sim1/X$. Its stationarity relation $Xa+a^2=1$ gives $\Phi_-(X,0)=-a/4-a^3/12\sim-1/(4X)$. Thus the minimized <free-energy density> becomes $-r^2/(4q)$ for fixed $q>0$ as $r\uparrow0$, recovering the ordinary quartic <continuous phase transition> and its <heat-capacity critical exponent> $\alpha=0$. Replacing the scaling function by a nonzero constant in this limit would give an incorrect exponent.
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