Analytic prediction of the exact thermodynamics of a first-order structural phase transition: A practical second-order self-consistent phonon theory

Abstract

We examine an extension of self-consistent phonon theory (SCPT) that allows for the explicit evaluation of second-order corrections to the free energy for both the high- and low-temperature phases for a system undergoing a first-order structural phase transition. The motivation for the inclusion of these terms stemmed from the many-body theory developed to treat the lattice vibrations in anharmonic crystals. This approach does not modify predictions for the phonon frequencies that would be observed by inelastic neutron scattering; however, we show that these higher-order contributions to the free energy are essential if the bulk limit of the equilibrium thermodynamic quantities are to be forecast accurately. Finite-size scaling is used to extrapolate the bulk limit, and we present arguments showing that precursor fluctuations are not allowed in bulk systems that are truly ergodic. Thus, in part the effectiveness of our second-order SCPT may be understood by noting the absence of large-amplitude fluctuations. In addition, dynamical structure factors, calculated using molecular-dynamic simulations, for systems of a strip geometry, show sharp phonon peaks at the SCPT frequencies, with lifetimes much longer than phonon periods–these lifetimes grow as one approaches the bulk limit.