An experiment-oriented analysis of 2D spin-glass dynamics: a twelve time-decades scaling study

TL;DR

This study uses extensive simulations to analyze the out-of-equilibrium dynamics of 2D spin glasses over twelve orders of magnitude in time, revealing a universal scaling behavior and critical dynamics near zero temperature.

Contribution

It provides the first comprehensive twelve-decade simulation of 2D spin-glass dynamics, demonstrating a universal scaling function and detailed divergence of the time-scale near zero temperature.

Findings

Domain growth follows a single scaling function.

Time-scale diverges as temperature approaches zero.

Barrier heights grow with critical dynamics.

Abstract

Recent high precision experimental results on spin-glass films ask for a detailed understanding of the domain-growth dynamics of two-dimensional spin glasses. To achieve this goal, we numerically simulate the out-equilibrium dynamics of the Ising spin glass for a time that spans close to twelve orders of magnitude (from picoseconds to order of a second), in systems large enough to avoid finite-size effects. We find that the time-growth of the size of the glassy domains is excellently described by a single scaling function. A single time-scale $\tau(T)$ controls the dynamics. $\tau(T)$ diverges upon approaching the $T=0$ critical point. The divergence of $\tau(T\to 0)$ is Arrhenius-like, with a barrier height that depends very mildly on temperature. The growth of this barrier-height is best described by critical dynamics. As a side product we obtain an impressive confirmation of universality of the equilibrium behavior of two-dimensional spin-glasses.