Environment Overwhelms both Nature and Nurture in a Model Spin Glass

TL;DR

This study investigates how the environment, initial conditions, and noise influence the evolution of spin glasses, revealing that environment dominates while initial states and noise histories leave distinct, scale-dependent imprints on the system's correlations.

Contribution

It introduces patchwork dynamics to simulate glassy behavior over large scales and demonstrates the dominant role of environment over initial conditions and noise in spin glass coarsening.

Findings

Correlations on most scales are environment-dependent.

Initial states influence domain wall structures during coarsening.

Correlations in identical initial states converge as a power law with scale.

Abstract

The microscopic dependence of glassy equilibration on sample history, both the initial configuration and the specific sequence of random noise, is examined. The temporal evolution of spin configurations in a two-dimensional Ising spin glass is simulated using patchwork dynamics, a coarse-grained heuristic for glassy dynamics, allowing simulations over a wide range of length scales. Most of the nearest-neighbor spin correlations are independent of the details of evolution, due to the formation of rigid domains. The correlations on a fractal set of domain walls are found to be variable and to depend distinctly on the noise history and the initial state. Correlations in samples with independent initial configurations are found to persistently differ when subject to identical noise histories, for coarsening scales of up to hundreds of lattice units. However, samples with identical initial configurations and subject to independent noise histories have correlations that converge to each other as a power law in scale. The initial "nature" of the state is retained in the domain walls during coarsening under distinct noises ("nurture"), while the location of the domain walls at each scale is determined by the frozen disorder ("environment"), independent of initial state or noise history. We also provide evidence that coarsening with local dynamics at finite temperature gives persistence of overlaps roughly consistent with coarsening at zero temperature.