First-principles model hamiltonians for ferroelectric phase transitions

Formal aspects of the construction of model Hamiltonians for the study of ferroelectric phase transitions are reviewed. It is demonstrated that first-principles linear-response calculations and total-energy calculations with symmetry-constrained ionic relaxation are very useful in the determination of the local mode variable and of an explicit expression for the model Hamiltonian. Results of first-principles pseudopotential calculations of the lattice constant, distortion energies and Born effective charges Z* for the perovskite ferroelectric PbTiO3 are discussed. A test of the model Hamiltonian approach through application to a minimal rigid ion model and comparison with Monte Carlo simulation is outlined, and preliminary results described.