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.

5 pages, 2 figures

References in corpus (8)

• Theoretical perspective on the glass transition and amorphous materials
• Fractal free energy landscapes in structural glasses
• 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
• Non-perturbative fixed point in a non-equilibrium phase transition
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions

Cited by in corpus (7)

• Absence of Marginal Stability in a Structural Glass
• Rejuvenation and Memory Effects in a Structural Glass
• Deconstructing the glass transition through critical experiments on colloids
• Low-temperature anomalies of a vapor deposited glass
• The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential
• The chemical bond as an emergent phenomenon
• Probing the Gardner transition in an active quasi-thermal pressure-controlled granular system