Holographic approach of the spinodal instability to criticality

TL;DR

This paper uses holography to study spinodal instabilities near and far from critical points, revealing how phase separation characteristics and formation times vary, and introduces a new criterion to distinguish inhomogeneous states.

Contribution

It provides a detailed holographic analysis of spinodal instabilities, including phase separation dynamics and a novel criterion for identifying different inhomogeneous states.

Findings

Wider phase separation near critical points.

Reduced formation time far from critical points.

Discovery of a new dissipation setup with peak-to-plateau transition.

Abstract

A smoking gun signature for a first-order phase transition with negative speed of sound squared $c_s^2$ is the occurrence of a spinodal instability. In the gauge/gravity duality it corresponds to a Gregory-Laflamme type instability, which can be numerically simulated as the evolution of unstable planar black branes. Making use of holography its dynamics is studied far from and near a critical point with the following results. Near a critical point the interface between cold and hot stable phases, given by its width and surface tension, is found to feature a wider phase separation and a smaller surface tension. Far away from a critical point the formation time of the spinodal instability is reduced. Across softer and harder phase transitions, it is demonstrated that mergers of equilibrated peaks and unstable plateaux lead to the preferred final single phase separated solution. Finally, a new atypical setup with dissipation of a peak into a plateau is discovered. In order to distinguish the inhomogeneous states I propose a new criterium based on the maximum of the transverse pressure at the interface which encodes phase-mixed peaks versus fully phase separated plateaux.