Scaling theory of the Mott transition and breakdown of the Gr\"uneisen scaling near a finite-temperature critical end point

TL;DR

This paper develops a scaling theory for lattice responses near a finite-temperature critical end point, revealing divergence in the Gr"uneisen ratio and applying it to experimental data on a layered organic conductor.

Contribution

It introduces a scaling framework for lattice responses near critical points and explicitly evaluates the scaling function for the 2D Ising universality class, connecting theory with experiments.

Findings

Thermal expansivity is more singular than specific heat near the critical point.

The Gr"uneisen ratio diverges as the critical point is approached.

Experimental data on layered organic conductors align with the theoretical predictions.

Abstract

We discuss a scaling theory of the lattice response in the vicinity of a finite-temperature critical end point. The thermal expansivity is shown to be more singular than the specific heat such that the Gr\"uneisen ratio diverges as the critical point is approached, except for its immediate vicinity. More generally, we express the thermal expansivity in terms of a scaling function which we explicitly evaluate for the two-dimensional Ising universality class. Recent thermal expansivity measurements on the layered organic conductor kappa-(BEDT-TTF)_2 X close to the Mott transition are well described by our theory.