The Gardner transition in finite dimensions

Abstract

Recent works on hard spheres in the limit of infinite dimensions revealed that glass states, envisioned as meta-basins in configuration space, can break up in a multitude of separate basins at low enough temperature or high enough pressure, leading to the emergence of new kinds of soft-modes and unusual properties. In this paper we study by perturbative renormalisation group techniques the critical properties of this transition, which has been discovered in disordered mean-field models in the '80s. We find that the upper critical dimension $d_u$ above which mean-field results hold is strictly larger than six and apparently non-universal, i.e. system dependent. Below $d_u$, we do not find any perturbative attractive fixed point (except for a tiny region of the 1RSB breaking parameter), thus showing that the transition in three dimensions either is governed by a non-perturbative fixed point unrelated to the Gaussian mean-field one or becomes first order or does not exist. We also discuss possible relationships with the behavior of spin glasses in a field.

arXiv comment5 pages, 2 figures

References in corpus (33)

• Theoretical perspective on the glass transition and amorphous materials
• Theory of Structural Glasses and Supercooled Liquids
• Fractal free energy landscapes in structural glasses
• The structural glass transition and the entropy of the metastable states
• Effects of compression on the vibrational modes of marginally jammed solids
• Geometric origin of excess low-frequency vibrational modes in amorphous solids
• On the nature of the low-temperature phase in discontinuous mean-field spin glasses
• Exact theory of dense amorphous hard spheres in high dimension. III. The full RSB solution
• Stability at Random Close Packing
• Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition
• Probing a liquid to glass transition in equilibrium
• Exact theory of dense amorphous hard spheres in high dimension. I. The free energy
• Geometric interpretation of pre-vitrification in hard sphere liquids
• Heterogeneous Dynamics, Marginal Stability and Soft Modes in Hard Sphere Glasses
• On the rigidity of a hard sphere glass near random close packing
• Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses
• Non-perturbative fixed point in a non-equilibrium phase transition
• Disappearance of the de Almeida-Thouless line in six dimensions
• Ising spin glass transition in magnetic field out of mean-field
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Replica symmetry breaking in and around six dimensions
• Replica-symmetry-breaking transitions and off-equilibrium dynamics
• Spin glass transition in a magnetic field: a renormalization group study
• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
• Generic replica symmetric field-theory for short range Ising spin glasses
• Dynamical transition in the D = 3 Edwards-Anderson spin glass in an external magnetic field
• First steps of a nucleation theory in disordered systems
• Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions
• p-spin model in finite dimensions and its relation to structural glasses
• The Thermodynamic Glass Transition in Finite Dimensions
• Continuous phase transition in a spin-glass model without time-reversal symmetry
• Numerical study of a short-range p-spin glass model in three dimensions
• Critical properties of a three dimensional p-spin model

Cited by in corpus (33)

• Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
• Growing timescales and lengthscales characterizing vibrations of amorphous solids
• Breakdown of Elasticity in Amorphous Solids
• A stability-reversibility map unifies elasticity, plasticity, yielding and jamming in hard sphere glasses
• Experimental evidences of the Gardner phase in a granular glass
• Absence of Marginal Stability in a Structural Glass
• Perspective: Gardner Physics in Amorphous Solids and Beyond
• Rejuvenation and Memory Effects in a Structural Glass
• Johari-Goldstein relaxation far below Tg: Experimental evidence for the Gardner transition in structural glasses?
• Numerical detection of the Gardner transition in a mean-field glass former
• Deconstructing the glass transition through critical experiments on colloids
• Nontrivial critical fixed point for replica-symmetry-breaking transitions
• The Gardner transition in physical dimensions
• Low-frequency vibrational spectrum of mean-field disordered systems
• Spin-glass--like aging in colloidal and granular glasses
• Marginally stable phases in mean-field structural glasses
• Hierarchical landscape of hard disk glasses
• Low-temperature anomalies of a vapor deposited glass
• Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class
• The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential
• Marginal stability of soft anharmonic mean field spin glasses
• Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning
• The chemical bond as an emergent phenomenon
• Active microrheology of a bulk metallic glass
• Impact of jamming criticality on low-temperature anomalies in structural glasses
• An exploratory study of the glassy landscape near jamming
• Searching for the Gardner transition in glassy glycerol
• A continuous constraint satisfaction problem for the rigidity transition in confluent tissues
• Field theory for zero temperature soft anharmonic spin glasses in a field
• Dynamic Gardner crossover in a simple structural glass
• The Gardner correlation length scale in glasses
• Probing the Gardner transition in an active quasi-thermal pressure-controlled granular system
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain