Independent anharmonic oscillator approximation in the theory of structural phase transitions in crystals

A new method in the microscopic theory of anharmonic crystal lattice dynami cs-the independent anharmonic oscillator (IAO) approximation-is discussed. The method is compared with traditional approaches (such as the mean-field and renormalized self-consistent phonon methods) from the standpoint of the analysis of the main approximations. Different methods are applied to the description of the structural phase transition in a monoatomic anharmonic c rystal, the results obtained are analyzed, and the numerical accuracy of di fferent approximations is estimated. It is demonstrated that, for this mode l in the displacement-type instability range, the new method, unlike the se lf-consistent phonon method, adequately describes the phase transition as a second-order transition. The phase transition temperature calculated in th e displacement limit monotonically tends to the exact value in contrast wit h the temperature obtained within the mean field approximation. (C) 2000 MA IK "Nauka/Interperiodica".