 Solution

Let $\Delta T=T-T_c$, with $a,c>0$ fixed. The equilibrium phase diagram has boundariesFor either branch, larger $\Delta T$ is disordered and smaller $\Delta T$ is ordered. Both signs of the ordered magnetization are symmetry-related global minima throughout the ordered region, rather than separate regions selected by temperature and $b$.

The branches meet at the tricritical point $(\Delta T,b)=(0,0)$. Directly on $b=0$, minimizing $r{m}^2+c{m}^6/3$ givesThe transition there remains continuous, with a different mean-field critical exponent. For $b<0$, the metastability boundaries are $\Delta T=0$ for the disordered state and $\Delta T=b^2/(4ac)$ for the ordered state. The first-order phase transition curve lies strictly between them, as shown in the figure. These spinodal curves describe possible hysteretic continuation of local minima, not equilibrium phase boundaries.