Dynamics and statistical mechanics of a one-dimensional model Hamiltonian for structural phase transitions

TLDR

The study investigates the thermodynamic and dynamic behavior of a strongly anharmonic one‑dimensional model Hamiltonian representative of displacive phase transitions. Thermodynamic properties are obtained exactly via functional‑integral methods without Hartree or decoupling approximations and without introducing artificial temperature dependence. Domain‑wall solutions dominate the dynamics, yielding low‑temperature thermodynamics that matches a phenomenological phonon‑plus‑domain‑wall model, with equal‑time correlations agreeing between methods and dynamic spectra exhibiting both phonon peaks and a central domain‑wall peak.

Abstract

We have studied thermodynamic and some dynamic properties of a one-dimensional-model system whose displacement field Hamiltonian is strongly anharmonic, and is representative of those used to study displacive phase transitions. By studying the classical equations of motion, we find important solutions (domain walls) which cannot be represented effectively by the usual phonon perturbation expansions. The thermodynamic properties of this system can be calculated exactly by functional integral methods. No Hartree or decoupling approximations are made nor is a temperature dependence of the Hamiltonian introduced artificially. At low temperature, the thermodynamic behavior agrees with that found from a phenomenological model in which both phonons and domain walls are included as elementary excitations. We then show that equal-time correlation functions calculated by both functional-integral and phenomenological methods agree, and that the dynamic correlation functions (calculated only phenomenologically) exhibit a spectrum with both phonon peaks and a central peak due to domain-wall motion.