Crossing a large-N phase transition at finite volume

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 → ∞, 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.

Holographic Bubbles with Jecco: Expanding, Collapsing and Critical

“…In these equations λ 4 and λ 6 are freely specifiable dimensionless parameters related to the parameters φ M and φ Q used in e.g. [60,39] through…”

“…Through holography, this approach has facilitated the study of far-from-equilibrium dynamics of strongly-coupled gauge theories, allowing for studies of isotropization [25][26][27], collisions of gravitational shockwaves (used as models for heavy-ion collisions) [28][29][30], momentum relaxation [31], turbulence [32], collisions in non-conformal theories [33,34], phase transitions and dynamics of phase separation [35][36][37][38][39][40][41], collisions in theories with phase transitions [42], dynamical instabilities [43], and even applications to gravitationalwave physics [44][45][46][47][48] and bubble dynamics [49,12,50,51]. See [52] for more references and a comprehensive overview of the techniques involved, and also [53][54][55] for equivalent approaches using Cauchy evolutions.…”

Gravitational waves from a holographic phase transition

“…It should be noted that all these studies are based on static configurations. Dynamical evolution of strongly coupled theories close to a phase transition has been studied in the context of applications to heavy ion collisions and condensed matter [44][45][46][47], including dynamical phase separation in three-dimensional [48][49][50] and four-dimensional [51][52][53] theories.…”

Holographic approach of the spinodal instability to criticality

“…If the simulated box contains enough total energy density, the final stage of the spinodal instability will be an inhomogeneous phase separated solution (neglecting for now subtleties of quite small finite boxes, where finite size effects act as regulator of the instability [52]) that forms a plateaux. In the special case of not enough total energy density in the system the formed final stage is a single peak.…”

“…With a field redefinition all stages of a strong spinodal instability and the hydrodynamization of shockwave collisions near a critical point were demonstrated to be described by hydrodynamics [49,51]. A recent analysis discusses the finite size effects [52] of the periodical longitudinal direction on the stability or instability of the plasma. A quite different setup involving plasma balls studies effects of the confined phase [53], but there is no spinodal region.…”