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It has been a long challenge to analytically construct the quantitativetemperature-dependent multi-well free-energy landscape over the space of orderparameters describing phase transitions and associated critical phenomena. Herewe propose a simple analytical model for the free energy landscape based on apriori concept of Boltzmann thermal mixing among multiple parabolic potentialsrepresenting different energetically degenerated ground states in contrast tothe popular Landau theory using the high-temperature disordered state as areference. The model recovers both the Weiss molecular field theory and thetemperature dependent behaviors of the second order Landau coefficient. It israther remarkable that such a simple analytical expression can describe a widevariety of properties across the ferroelectric phase transition in PbTiO3,including the temperature dependences of the spontaneous polarization, the heatcapacities, the permittivity tensor, and the lattice parameters. The approachalso allows parametrization of the free energy function across phasetransitions based directly on the 0 K thermodynamics data that can be obtainedfrom DFT calculations. We anticipate that the approach can be equally appliedto other types of critical phenomena, e.g., the superconducting phasetransition, the metal-insulator transition, and the magnetic transitions.

Temperature-dependent Multi-well Free-energy Landscape for Phase Transitions: PbTiO3 as a Prototype