Quartic Landau equilibrium branches

For $f=f_0+a(T-T_c)q^2/2+b{q}^4/4$ with $a,b>0$, the minimum is $q=0$ above $T_c$ and $q=\pm \sqrt{a(T_c-T)/b}$ below it. The stationary solutions must be checked for stability; below $T_c$ the central solution is a maximum.