Abstract
It is shown how the self-consistent phonon Ansatz leads to a new class of exactly soluble models of a structural phase transition. Both nonpolynomial anharmonicity and disorder are analyzed in detail. In the classical limit, the thermodynamics is obtained and sufficient conditions on the anharmonicity are given to ensure a soft-mode phase transition. Diagonal disorder has been studied numerically. It is found that in three dimensions a pronounced mobility edge, separating localized and delocalized phonon states, may exist.
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van Hemmen, J.L., Zagrebnov, V.A. Models of a structural phase transition with general anharmonicity and disorder. J Stat Phys 53, 835–852 (1988). https://doi.org/10.1007/BF01014228
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DOI: https://doi.org/10.1007/BF01014228