Critical elasticity at zero and finite temperature

TL;DR

This paper reviews elastic phase transitions in crystals at zero and finite temperatures, highlighting how long-range shear forces influence critical fluctuations and lead to unique quantum and classical critical behaviors.

Contribution

It provides a comprehensive analysis of how elastic interactions suppress critical fluctuations, resulting in Gaussian fixed points or mean-field behavior at quantum and classical phase transitions.

Findings

Critical fluctuations are suppressed by long-range shear forces.

Quantum phase transitions exhibit critical phonon thermodynamics with a stable Gaussian fixed point.

Solid-solid critical end points show mean-field critical behavior without diverging correlation length.

Abstract

Elastic phase transitions of crystals and phase transitions whose order parameter couples linearly to elastic degrees of freedom are reviewed with particular focus on instabilities at zero temperature. A characteristic feature of these transitions is the suppression of critical fluctuations by long-range shear forces. As a consequence, at an elastic crystal symmetry-breaking quantum phase transition the phonon velocity vanishes only along certain crystallographic directions giving rise to critical phonon thermodynamics described by a stable Gaussian fixed point. At an isostructural solid-solid quantum critical end point, on the other hand, the complete suppression of critical fluctuations results in true mean-field critical behavior without a diverging correlation length. Whenever an order parameter couples bilinearly to the strain tensor, the critical properties are eventually governed by critical crystal elasticity. This is, for example, the case for quantum critical metamagnetism but also for the classical critical Mott end point at finite $T$. We discuss and compare the solid-solid end points expected close to the Mott transition in V$_2$O$_3$ and $\kappa$-(BEDT-TTF)$_2 X$.