A1  ^?? Write down the conditions for a local energy minimum, if energy is given by equation $(1)$. For which values of $T$ the spontaneous polarization would be possible?

A2  ^?? Derive an equation for equilibrium values of spontaneous polarization, $P_0$.

A3  ^?? Expression from the previous task simplifies significantly in the limit $T\to T_0$. Find the values of $P_0$ in this limit. Express your answer in terms of $\alpha$, $\beta$ and $\Delta T=T_0-T$.

B1  ^?? Derive an expression for the electric susceptibility of a spontaneously polarized ferroelectric.