  It has been a grand challenge to resolve the temperature evolution of
multi-well free-energy landscape which is fundamentally relevant to phase
transitions and associated critical phenomena as listed by Ginzburg [Rev. Mod.
Phys. 76 (2004) 981]. To address this challenge, here we provide a simple
solution based on a priori concept of Boltzmann thermal mixing among multiple
parabolic potentials. The success and the impact of the present approach have
been extensively demonstrated using a variety of materials, including Nb,
YBa2Cu3O(7-x), Ca3Ru2O7, Ni, BiFeO3, and PbTiO3.
