Nature vs. Nurture: Dynamical Evolution in Disordered Ising Ferromagnets

Abstract

We study the predictability of zero-temperature Glauber dynamics in various models of disordered ferromagnets. This is analyzed using two independent dynamical realizations with the same random initialization (called twins). We derive, theoretically and numerically, trajectories for the evolution of the normalized magnetization and twin overlap as the system size tends to infinity. The systems we treat include mean-field ferromagnets with light-tailed and heavy-tailed coupling distributions, as well as highly-disordered models with a variety of other geometries. In the mean-field setting with light-tailed couplings, the disorder averages out and the limiting trajectories of the magnetization and twin overlap match those of the homogenous Curie--Weiss model. On the other hand, when the coupling distribution has heavy tails, or the geometry changes, the effect of the disorder persists in the thermodynamic limit. Nonetheless, qualitatively all such random ferromagnets share a similar time evolution for their twin overlap, wherein the two twins initially decorrelate, before either partially or fully converging back together due to the ferromagnetic drift.

arXiv comment16 pages, 7 figures

References in corpus (8)

• Theory of Phase Ordering Kinetics
• The spherical 2+p spin glass model: an analytically solvable model with a glass-to-glass transition
• The spherical $2+p$ spin glass model: an exactly solvable model for glass to spin-glass transition
• Ground State Structure in a Highly Disordered Spin Glass Model
• Nature vs. Nurture: Predictability in Low-Temperature Ising Dynamics
• p>2 spin glasses with first order ferromagnetic transitions
• Zero-temperature dynamics in the dilute Curie-Weiss model
• Long-Time Predictability in Disordered Spin Systems Following a Deep Quench