Crossing a large-$N$ phase transition at finite volume

TL;DR

This paper uses holography to explore how finite volume affects phase transitions in a strongly coupled gauge theory, revealing inhomogeneous states, phase transitions, and stability properties of black brane solutions.

Contribution

It uncovers a variety of inhomogeneous states and phase transitions at finite volume in a holographic gauge theory, extending the understanding of phase behavior beyond infinite-volume limits.

Findings

Discovery of inhomogeneous, phase-separated states at finite volume.

Identification of first- and second-order phase transitions between these states.

Demonstration of stability properties and non-linear evolution of unstable states.

Abstract

The existence of phase-separated states is an essential feature of infinite-volume systems with a thermal, first-order phase transition. At energies between those at which the phase transition takes place, equilibrium homogeneous states are either metastable or suffer from a spinodal instability. In this range the stable states are inhomogeneous, phase-separated states. We use holography to investigate how this picture is modified at finite volume in a strongly coupled, four-dimensional gauge theory. We work in the planar limit, $N \to \infty$, which ensures that we remain in the thermodynamic limit. We uncover a rich set of inhomogeneous states dual to lumpy black branes on the gravity side, as well as first- and second-order phase transitions between them. We establish their local (in)stability properties and show that fully non-linear time evolution in the bulk takes unstable states to stable ones.