An effective Hamiltonian scheme is developed to study finite-temperature properties of multiferroic BiFeO3. This approach reproduces very well (i) the symmetry of the ground state, (ii) the Néel and Curie temperatures, and (iii) the intrinsic magnetoelectric coefficients (that are very weak). This scheme also predicts (a) an overlooked phase above Tc approximately 1100 K that is associated with antiferrodistortive motions, as consistent with our additional x-ray diffractions, (b) improperlike dielectric features above Tc, and (c) that the ferroelectric transition is of first order with no group-subgroup relation between the paraelectric and polar phases.
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