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An effective Hamiltonian for the ferroelectric transition in PbTiO3 isconstructed from first-principles density-functional-theory total-energy andlinear-response calculations through the use of a localized, symmetrized basisset of ``lattice Wannier functions.'' Explicit parametrization of the polarlattice Wannier functions is used for subspace projection, addressing theissues of LO-TO splitting and coupling to the complementary subspace. Incontrast with ferroelectric BaTiO3 and KNbO3, we find significant involvementof the Pb atom in the lattice instability. Monte Carlo simulations for thisHamiltonian show a first-order cubic-tetragonal transition at 660 K. Resultingtemperature dependence of spontaneous polarization, c/a ratio and unit-cellvolume near the transition are in good agreement with experiment. Comparison ofMonte Carlo results with mean field theory analysis shows that both strain andfluctuations are necessary to produce the first order character of thistransition.Comment: LateX file, 32 pages, 10 figure

physical review. b, condensed matter

Ab initio statistical mechanics of the ferroelectric phase transition in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">PbTiO</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Ab initio statistical mechanics of the ferroelectric phase transition inPbTiO3