Low-temperature structural phase transitions: Phonon-like and relaxation order-parameter dynamics

TL;DR

This paper presents a theoretical analysis of low-temperature structural phase transitions, exploring both phonon-like and relaxation order-parameter dynamics, with new insights into susceptibility behavior and the effects of long-range interactions.

Contribution

It introduces the first study of relaxation order-parameter dynamics at low temperatures and compares it to phonon-like behavior, highlighting differences in susceptibility asymptotics.

Findings

Relaxation dynamics show susceptibility ∼ (T^2 - T_c^2)^{-1} at low temperatures.

Long-range interactions do not alter the relaxation asymptotics.

Phonon-like and relaxation dynamics exhibit distinct temperature dependence behaviors.

Abstract

A theoretical study on low-temperature structural phase transitions is presented, in which both phonon-like and relaxation order-parameter dynamics are contemplated. While the first limiting case has been considered previously, the second one is studied here for the first time. Attention is put on the low-temperature asymptotics of the temperature dependence of the generalized susceptibility. In the relaxation case, it is found $\sim (T^2 - T_c^2)^{-1}$ for temperature-independent relaxation times in a broad region of the temperature-pressure phase diagram. In contrast to the obtained in the phonon-like case, this asymptotics is not modified by long-range interactions (dipolar forces, piezoelectric effect, etc.).