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The study of critical phenomena and phase transitions is an important part ofmodern condensed matter physics. In this regard, the phenomenological Landautheory has been extraordinarily useful. Hereby we present an alternativetheoretical description to the Landau theory for a system under phasetransition, based on a priori assumption that the macroscopic system is made ofthe thermal mixing among multi harmonics each of them can be distinguished bycrystal orientation, polar direction, magnetic direction, or even momentum etc.Our theory naturally gives rise to a long range field and is able to accountfor both the type of lattice and the spatial dimensionality, in addition tothat the excess free energy is referenced to the low temperature structuretogether with the positive excess entropy. The improvements over the Landautheory are demonstrated using ferroelectric-paraelectric system of PbTiO3 onits phase transition and associated thermodynamic behaviors.

A Thermal Harmonic Field Description of Phase Transition: The Alternative Approach to the Landau Theory