On low-temperature structural phase transitions

TL;DR

This paper examines zero- and low-temperature structural phase transitions, highlighting the limitations of current models in accurately describing quantum and thermal fluctuations and questioning the assumptions of continuous medium theories.

Contribution

It analyzes the effects of quantum and thermal fluctuations on low-temperature phase transitions within a classical model, revealing limitations of existing dynamic theories and continuous medium approaches.

Findings

Quantum fluctuations significantly affect low-temperature phase behavior.

Current models lack a realistic high-temperature dynamics description.

Continuous medium theories have notable shortcomings at low temperatures.

Abstract

We comment on zero- and low-temperature structural phase transitions, expecting that these comments might be relevant not only for this structural case. We first consider a textbook model whose classical version is the only model for which the Landau theory of phase transitions and the concept of ``soft mode'' introduced by Ginzburg are exact. Within this model, we reveal the effects of quantum fluctuations and thermal ones at low temperatures. To do so, the knowledge of the dynamics of the model is needed. However, as already was emphasized by Ginzburg et al. in eighties, a realistic theory for such a dynamics at high temperatures is lacking, what also seems to be the case in the low temperature regime. Consequently, some theoretical conclusions turn out to be dependent on the assumptions on this dynamics. We illustrate this point with the low-temperature phase diagram, and discuss some unexpected shortcomings of the continuous medium approaches.