Rethinking mean-field glassy dynamics and its relation with the energy landscape: the awkward case of the spherical mixed p-spin model

Abstract

The spherical p-spin model is not only a fundamental model in statistical mechanics of disordered system, but has recently gained popularity since many hard problems in machine learning can be mapped on it. Thus the study of the out of equilibrium dynamics in this model is interesting both for the glass physics and for its implications on algorithms solving NP-hard problems. We revisit the long-time limit of the out of equilibrium dynamics of mean-field spherical mixed p-spin models. We consider quenches (gradient descent dynamics) starting from initial conditions thermalized at some temperature in the ergodic phase. We perform numerical integration of the dynamical mean-field equations of the model and we find an unexpected dynamical phase transition. Below an onset temperature, higher than the dynamical transition temperature, the asymptotic energy goes below the "threshold energy" of the dominant marginal minima of the energy function and memory of the initial condition is kept. This behavior, not present in the pure spherical p-spin model, resembles closely the one observed in simulations of glass-forming liquids. We then investigate the nature of the asymptotic dynamics, finding an aging solution that relaxes towards deep marginal minima, evolving on a restricted marginal manifold. Careful analysis, however, rules out simple aging solutions. We compute the constrained complexity in the aim of connecting the asymptotic solution to the energy landscape.

References in corpus (31)

• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Theoretical perspective on the glass transition and amorphous materials
• Parallel Tempering: Theory, Applications, and New Perspectives
• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
• Supercooled Liquids for Pedestrians
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Fractal free energy landscapes in structural glasses
• Spin-Glass Theory for Pedestrians
• Inherent Structure Entropy of Supercooled Liquids
• Recipes for metastable states in Spin Glasses
• Measuring equilibrium properties in aging systems
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• On the nature of the low-temperature phase in discontinuous mean-field spin glasses
• On the stationary points of the TAP free energy
• Complexity of random smooth functions on the high-dimensional sphere
• Pinching a glass reveals key properties of its soft spots
• Dynamics within metastable states in a mean-field spin glass
• On the cooling-schedule dependence of the dynamics of mean-field glasses
• Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses
• On Mean Field Glassy Dynamics out of Equilibrium
• The spherical $2+p$ spin glass model: an exactly solvable model for glass to spin-glass transition
• Perspective: Gardner Physics in Amorphous Solids and Beyond
• Effect of instantaneous and continuous quenches on the density of vibrational modes in model glasses
• The geometry of the Gibbs measure of pure spherical spin glasses
• The dynamics of the spherical p-spin model: from microscopic to asymptotics
• Determination of onset temperature from the entropy for fragile to strong liquids
• A statics-dynamics equivalence through the fluctuation-dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements
• Off-equilibrium confined dynamics in a glassy system with level-crossing states
• Following states in temperature in the spherical s+p-spin glass model
• Precursors of the Spin Glass Transition in Three Dimensions

Cited by in corpus (40)

• Generalized Lotka-Volterra equations with random, non-reciprocal interactions: the typical number of equilibria
• Low-frequency vibrational spectrum of mean-field disordered systems
• A jamming plane of sphere packings
• Relaxation dynamics in the energy landscape of glass-forming liquids
• Memory formation in jammed hard spheres
• Gradient descent dynamics in the mixed $p$-spin spherical model: finite size simulation and comparison with mean-field integration
• Dynamical Instantons and Activated Processes in Mean-Field Glass Models
• Path Integral Approach Unveils the Role of Complex Energy Landscape for Activated Dynamics of Glassy Systems
• On weak ergodicity breaking in mean-field spin glasses
• How to count in hierarchical landscapes: a 'full' solution to mean-field complexity
• The Loss Surfaces of Neural Networks with General Activation Functions
• Arrangement of nearby minima and saddles in the mixed spherical energy landscapes
• A spin-glass model for the loss surfaces of generative adversarial networks
• Random features and polynomial rules
• Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model
• Jamming, relaxation, and memory in a structureless glass former
• Low energy excitations of mean-field glasses
• Dynamical mean field theory for models of confluent tissues and beyond
• Spin-glass dynamics: experiment, theory and simulation
• Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures
• Numerical renormalization of glassy dynamics
• Entropic barriers as a reason for hardness in both classical and quantum algorithms
• On-Site Potential Creates Complexity in Systems with Disordered Coupling
• Glass--like transition described by toppling of stability hierarchy
• Competition between Barrier- and Entropy-Driven Activation in Glasses
• Instantaneous normal modes of glass-forming liquids during the athermal relaxation process of the steepest descent algorithm
• Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models
• Thermodynamics of the Fredrickson-Andersen Model on the Bethe Lattice
• Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
• Multiple transitions in an infinite range p-spin random-crystal field Blume Capel model
• Analytic continuation over complex landscapes
• On the topology of solutions to random continuous constraint satisfaction problems
• K-core attack, equilibrium K-core, and kinetically constrained spin system
• Recursive Algorithm to the Centroid of Free Area for Inherent Structure and Hopping Motion in Deeply Supercooled Binary Hard Disk Systems
• Algorithmic thresholds in combinatorial optimization depend on the time scaling
• Strong ergodicity breaking in dynamical mean-field equations for mixed p-spin glasses
• Controlling the Glass Transition through Active Fluctuating Interactions
• Rare Trajectories in a Prototypical Mean-field Disordered Model: Insights into Landscape and Instantons
• Gradient descent dynamics and the jamming transition in infinite dimensions
• Rényi complexity in mean-field disordered systems