= Critical endpoint of a quartic Landau free energy
{title2=$f'=f''=f'''=0$}
For the stable scalar <Landau free energy> $f=b\lambda^4+c\lambda^3+a\lambda^2+d\lambda$, $b>0$, a stable zero-curvature equilibrium must have $f'=f''=f'''=0$. Solving these equations gives
$$
\lambda_c=-\frac c{4b},\qquad a_c=\frac{3c^2}{8b},\qquad d_c=\frac{c^3}{16b^2}.
$$
At this point $f=f(\lambda_c)+b(\lambda-\lambda_c)^4$. Varying two control parameters allows a line of <first-order phase transitions> to terminate here. A <spinodal point> satisfies zero curvature but need not satisfy the third-derivative condition or remain a local minimum.
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