  A method for the calculation of the temperature dependence of dielectric and
piezoelectric responses, based on the use of a first-principles effective
Hamiltonian, is described. Results are presented for the ferroelectric
perovskite PbTiO3. While the method includes only the soft-mode contributions
to the responses, it is argued to give a good description of the divergences or
near-divergences of the response functions near the cubic-tetragonal
transition. The expression of the response functions in terms of correlation
functions is used to provide a real-space interpretation of the responses which
clearly distinguishes between PbTiO3 and the related materials BaTiO3 and
KNbO3.
