Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution

Abstract

We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way towards a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.

6 pages, 3 figures, submitted to PNAS

References in corpus (11)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Fractal free energy landscapes in structural glasses
• Jamming versus Glass Transitions
• Jamming Criticality Revealed by Removing Localized Buckling Excitations
• The simplest model of jamming
• Excess Vibrational Modes and the Boson Peak in Model Glasses
• Geometric interpretation of pre-vitrification in hard sphere liquids
• Dynamic criticality at the jamming transition
• On asymptotics of eigenvectors of large sample covariance matrix
• A microscopic mean-field theory of the jamming transition
• Unearthing the anticrystal: criticality in the linear response of disordered solids

Cited by in corpus (124)

• Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
• Continuum limit of the vibrational properties of amorphous solids
• Statistics and properties of low-frequency vibrational modes in structural glasses
• Low-frequency vibrational modes of stable glasses
• Scaling description of generalization with number of parameters in deep learning
• Local inversion-symmetry breaking controls the boson peak in glasses and crystals
• The simplest model of jamming
• Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems
• Universal non-phononic density of states in 2D, 3D and 4D glasses
• Breakdown of Elasticity in Amorphous Solids
• The jamming transition as a paradigm to understand the loss landscape of deep neural networks
• Pinching a glass reveals key properties of its soft spots
• Universality of the nonphononic vibrational spectrum across different classes of computer glasses
• Universal non-Debye scaling in the density of states of amorphous solids
• Low-energy quasilocalized excitations in structural glasses
• Does a growing static length scale control the glass transition?
• Phonon transport and vibrational excitations in amorphous solids
• A jamming transition from under- to over-parametrization affects loss landscape and generalization
• Absence of Marginal Stability in a Structural Glass
• Fast generation of ultrastable computer glasses by minimization of an augmented potential energy
• A characteristic energy scale in glasses
• Universality of jamming of non-spherical particles
• Perspective: Gardner Physics in Amorphous Solids and Beyond
• Anomalous vibrational properties in the continuum limit of glasses
• Probing the non-Debye low frequency excitations in glasses through random pinning
• Theory for Swap Acceleration near the Glass and Jamming Transitions
• Soft Modes, Localization and Two-Level Systems in Spin Glasses
• Frustration-induced internal stresses are responsible for quasilocalized modes in structural glasses
• Out-of-equilibrium dynamical mean-field equations for the perceptron model
• Low-frequency vibrational spectrum of mean-field disordered systems
• Jamming in multilayer supervised learning models
• Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids
• Liu-Nagel phase diagrams in infinite dimension
• Spin-glass--like aging in colloidal and granular glasses
• Relaxation and vibrational properties in metal alloys and other disordered systems
• Mean-field model for the density of states of jammed soft spheres
• Boson-peak vibrational modes in glasses feature hybridized phononic and quasilocalized excitations
• Low-frequency vibrations of jammed packings in large spatial dimensions
• Marginally stable phases in mean-field structural glasses
• Finite-size effects in the nonphononic density of states in computer glasses
• Detection of boson peak and fractal dynamics of disordered system using terahertz spectroscopy
• Hierarchical landscape of hard disk glasses
• Critical jammed phase of the linear perceptron
• Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems
• Vibrational properties of hard and soft spheres are unified at jamming
• Low-frequency excess vibrational modes in two-dimensional glasses
• The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential
• Mean-field model of interacting quasilocalized excitations in glasses
• Vibrational density of states and specific heat in glasses from random matrix theory
• Marginal stability of soft anharmonic mean field spin glasses
• Hessian spectrum at the global minimum of high-dimensional random landscapes
• Universal relaxation dynamics of sphere packings below jamming
• Hydrodynamics of disordered marginally-stable matter
• Universal non-mean-field scaling in the density of state of amorphous solids
• Experimental observation of the marginal glass phase in a colloidal glass
• Vibrational spectrum derived from the local mechanical response in disordered solids
• Theory of superconductivity mediated by Rashba coupling in incipient ferroelectrics
• The nature of non-phononic excitations in disordered systems
• Mean-field caging in a random Lorentz gas
• Evidence for marginal stability in emulsions
• A unifying model for random matrix theory in arbitrary space dimensions
• Experimental observations of marginal criticality in granular materials
• On the Dynamics of Glassy Systems
• Disorder-free spin glass transitions and jamming in exactly solvable mean-field models
• Impact of jamming criticality on low-temperature anomalies in structural glasses
• Searching for the Gardner transition in glassy glycerol
• Density of States below the First Sound Mode in 3D Glasses
• Disorder-induced vibrational anomalies from crystalline to amorphous solids
• Vibrational phenomena in glasses at low temperatures captured by field theory of disordered harmonic oscillators
• Critical energy landscape of linear soft spheres
• Delocalization transition in low energy excitation modes of vector spin glasses
• Quantum Jamming: Critical Properties of a Quantum Mechanical Perceptron
• Complete mathematical theory of the jamming transition: A perspective
• Mean-field description for the architecture of low-energy excitations in glasses
• Analysis of vibrational normal modes for Coulomb clusters
• Low-Frequency Vibrational States in Ideal Glasses with Random Pinning
• Non-phononic density of states of two-dimensional glasses revealed by random pinning
• Introduction to the dynamics of disordered systems: equilibrium and gradient descent
• Higher order corrections to the effective potential close to the jamming transition in the perceptron model
• Jamming Criticality of Near-Crystals
• A continuous constraint satisfaction problem for the rigidity transition in confluent tissues
• Jamming and replica symmetry breaking of weakly disordered crystals
• Mean field theory of jamming of nonspherical particles
• Surfing on minima of isostatic landscapes: avalanches and unjamming transition
• Bose-Einstein-Like condensation of deformed random matrix: A replica approach
• High dimensional optimization under non-convex excluded volume constraints
• Force balance controls the relaxation time of the gradient descent algorithm in the satisfiable phase
• Edge Mode Amplification in Disordered Elastic Networks
• Ground State Stability and the Nature of the Spin Glass Phase
• Hard-Sphere Jamming through the Lens of Linear Optimization
• Localization in random bipartite graphs: numerical and empirical study
• Low energy excitations of mean-field glasses
• Quasi-localized vibrational modes, Boson peak and sound attenuation in model mass-spring networks
• Jamming and Unusual Charge Density Fluctuations of Strange Metals
• Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling
• Field theory for zero temperature soft anharmonic spin glasses in a field
• Novel elastic instability of amorphous solids in finite spatial dimensions
• Vibrational density of states of jammed packing: mean-field theory
• Level statistics and Anderson delocalization in two-dimensional granular materials
• Scaling regimes and fluctuations of observables in computer glasses approaching the unjamming transition
• Scaling collapse at the jamming transition
• Low frequency Raman study of the Boson peak in a Tellurite-tungstate glass over temperature
• Universal scaling for disordered viscoelastic matter near the onset of rigidity
• Enhanced Vibrational Stability in Glass Droplets
• Structural and mechanical characteristics of sphere packings near the jamming transition: From fully amorphous to quasi-ordered structures
• Testing the Heterogeneous-Elasticity Theory for low-energy excitations in structural glasses
• Manifolds pinned by a high-dimensional random landscape: Hessian at the global energy minimum
• Proliferation of non-linear excitations in the piecewise-linear perceptron
• Dynamic Gardner crossover in a simple structural glass
• Perspective: A Phase Diagram for Deep Learning unifying Jamming, Feature Learning and Lazy Training
• Self-planting: digging holes in rough landscapes
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Soft modes in vector spin glass models on sparse random graphs
• Two-level systems and harmonic excitations in a mean-field anharmonic quantum glass
• Critical properties of disordered XY model on sparse random graphs
• Noncrossing partition flow and random matrix models
• Further testing the validity of generalized heterogeneous-elasticity theory for low-frequency excitations in structural glasses
• Fluctuation Distributions of Energy Minima in Complex Landscapes
• Does mesoscopic elasticity control viscous slowing down in glassforming liquids?
• Scaling of Memories and Crossover in Glassy Magnets
• Particle pinning as a method to manipulate marginal stability
• Gradient descent dynamics and the jamming transition in infinite dimensions
• Critical fluctuations of elastic moduli in jammed solids
• Critical properties of the SAT/UNSAT transitions in the classification problem of structured data