Correlated-effective-field theory: A statistical approach for grossly anharmonic lattice vibrations

A correlated-effective-field theory is defined for interacting oscillators each moving in a local potential well of arbitrary form. Correlations are introduced into an effective-field framework and determined by forcing a consistency with the fluctuation theorem. The theory is formulated for both ordered and disordered phases as a model for a structural phase transition. In the limit of a quasiharmonic local potential the linearized theory is shown to be formally equivalent to self-consistent phonon theory for classical motion. In an opposite limit of extreme anharmonicity, with a deep-double-well local potential, the method is compared to Ising theory and shown to be equivalent to the spherical approximation.