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The analytical solutions of spontaneous polarization, phase transition temperature TC, and ferroelectric limit temperature Th have been solved based on the Landau-Devonshire eight-order potential. According to the analytical solutions, the eighth-order potential gives a more reasonable and thinner superheating zone (Th-TC). The analytical solutions can be applied to deduce other analytical solutions of the functional properties directly, e. g., dielectric susceptibility and pyroelectric coefficient. It can also be used to evaluate different Landau-Devonshire potentials as demonstrated for BaTiO3. [ABSTRACT FROM AUTHOR]