Maximum-energy records in glassy energy landscapes

Abstract

We study the evolution of the maximum energy $E_\max(t)$ reached between time $0$ and time $t$ in the dynamics of simple models with glassy energy landscapes, in instant quenches from infinite temperature to a target temperature $T$. Through a detailed description of the activated dynamics, we are able to describe the evolution of $E_\max(t)$ from short times, through the aging regime, until after equilibrium is reached, thus providing a detailed description of the long-time dynamics. Finally, we compare our findings with numerical simulations of the $p$-spin glass and show how the maximum energy record can be used to identify the threshold energy in this model.

arXiv comment22 pages, 5 figures; revised presentation

References in corpus (18)

• Level-Spacing Distributions and the Airy Kernel
• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Supercooled Liquids for Pedestrians
• On Orthogonal and Symplectic Matrix Ensembles
• Models of traps and glass phenomenology
• Spin-Glass Theory for Pedestrians
• Aging on Parisi's tree
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy--Widom limits and rates of convergence
• Solution of the dynamics of liquids in the large-dimensional limit
• Aging in the random energy model
• Replica-symmetry-breaking transitions and off-equilibrium dynamics
• Activated processes and Inherent Structure dynamics of finite-size mean-field models for glasses
• Record Dynamics: Direct Experimental Evidence from Jammed Colloids
• Comparing extremal and thermal Explorations of Energy Landscapes
• Activated Aging Dynamics and Effective Trap Model Description in the Random Energy Model
• Relaxation dynamics of the Ising $p$-spin disordered model with finite number of variables
• The mean field infinite range p=3 spin glass: equilibrium landscape and correlation time scales
• Activated dynamics: an intermediate model between REM and p-spin

Cited by in corpus (4)

• Path Integral Approach Unveils the Role of Complex Energy Landscape for Activated Dynamics of Glassy Systems
• Barriers, trapping times and overlaps between local minima in the dynamics of the disordered Ising $p$-spin Model
• Effective Trap-like Activated Dynamics in a Continuous Landscape
• Competition between Barrier- and Entropy-Driven Activation in Glasses