Analysis of landscape hierarchy during coarsening and aging in Ising spin glasses
arXiv:2009.03412 · doi:10.1103/PhysRevB.103.024201
Abstract
We use record dynamics (RD), a coarse-grained description of the ubiquitous relaxation phenomenology known as "aging", as a diagnostic tool to find universal features that distinguish between the energy landscapes of Ising spin models and the ferromagnet. According to RD, a non-equilibrium system after a quench relies on fluctuations that randomly generate a sequence of irreversible record-sized events (quakes or avalanches) that allow the system to escape ever-higher barriers of meta-stable states within a complex, hierarchical energy landscape. Once these record events allow the system to overcome such barriers, the system relaxes by tumbling into the following meta-stable state that is marginally more stable. Within this framework, a clear distinction can be drawn between the coarsening dynamics of an Ising ferromagnet and the aging of the spin glass, which are often put in the same category. To that end, we interpolate between the spin glass and ferromagnet by varying the admixture of ferromagnetic over anti-ferromagnetic bonds from the glassy state (at 50% each) to wherever clear ferromagnetic behavior emerges. The accumulation of record events grows logarithmic with time in the glassy regime, with a sharp transition at a specific admixture into the ferromagnetic regime where such activations saturate quickly. We show this effect both for the Edwards-Anderson model on a cubic lattice as well as the Sherrington-Kirkpatrick (mean-field) spin glass. While this transition coincides with a previously observed zero-temperature equilibrium transition in the former, that transition has not yet been described for the latter.
arXiv comment8 pages, RevTex4, some improved explanations, related information can be found at http://www.physics.emory.edu/faculty/boettcher/
References in corpus (26)
- Fractal free energy landscapes in structural glasses
- Separation of time and length scales in spin-glasses: temperature as a microscope
- Critical parameters of the three-dimensional Ising spin glass
- Random Costs in Combinatorial Optimization
- Logarithmically slow domain growth in nonrandomly frustrated systems: Ising models with competing interactions
- Heterogeneous Dynamics of Coarsening Systems
- Separation of time-scales and reparametrization invariance for aging systems
- Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model. I. Energy Relaxation and Domain Coarsening
- Log-Poisson statistics and full aging in glassy systems
- Ground-state behavior of the 3d +/-J random-bond Ising model
- A Crash Course on Aging
- The lid method for exhaustive exploration of metastable states of complex systems
- Intermittency, aging and record fluctuations
- Extension to order of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices
- Hierarchical landscape of hard disk glasses
- Energy and entropy of metastable states in glassy systems
- Record Dynamics: Direct Experimental Evidence from Jammed Colloids
- Comparing extremal and thermal Explorations of Energy Landscapes
- Exploring Valleys of Aging Systems: The Spin Glass Case
- Statistical Physics of the Glass Phase
- Free energy landscapes, dynamics and the edge of chaos in mean-field models of spin glasses
- Ageing at the Spin-Glass/Ferromagnet Transition: Monte Carlo Simulation using GPUs
- How to evaluate ground-state landscapes of disordered systems thermodynamical correctly
- Mesoscopic real space structures in aging spin-glasses: the Edwards-Anderson model
- Temporal and spatial heterogeneity in aging colloids: a mesoscopic model
- Intermittent relaxation in hierarchical energy landscapes