Abstract
An exact treatment of a cooperative Jahn-Teller transition is presented. The results are expressed in terms of the thermodynamic properties of the Ising model. The dynamic behavior of fluctuations is discussed in terms of irreversible thermodynamics. I. INTRODUCI'ION II. FREE ENERGY Models describing cooperative Jahn-Teller transitions have for the most part been treated in the random-phase approximation (RPA). ' 4 In RPA, the static thermal averages are determined in the mean-field approximation, while the dynamic behavior is described by equations of motion linearized about the mean-field values. A somewhat improved approximation, which has been considered by Halperin, is applicable under certain conditions for the case of two nondegenerate electronic levels. ' In the present paper an exact statistical mechanical treatment is given for a model containing all the essential features of the cooperative Jahn-Teller transition. The results are expressed in terms of the statistical mechanical properties of the Ising model. The model describes the interaction of a doubly degenerate electronic level at each lattice site with nondegenerate elastic strain and optic phonons of a given symmetry (at q = 0). Only a linear coupling between the phonons and the electronic system wi)l be considered. The Hamiltonian then takes the form'
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