Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses

TL;DR

This paper demonstrates that large scaling corrections are necessary to accurately describe droplet energies in two-dimensional spin glasses, improving the droplet model's applicability to numerical simulations.

Contribution

It introduces a modified droplet energy scaling law including a correction term, enhancing the understanding of spin glass behavior in two and three dimensions.

Findings

Scaling correction l^{-} is essential for accurate droplet energy description.

Modified scaling law explains previous simulation results.

Improves the droplet model's relevance to numerical data.

Abstract

The energy of a droplet of linear extent l in the droplet theory of spin glasses goes as l^{\theta} for large l. It is shown by numerical studies of large droplets in two-dimensional systems that this formula needs to be modified by the addition of a scaling correction l^{-\omega} in order to accurately describe droplet energies at the length scales currently probed in numerical simulations. Using this simple modification it is now possible to explain many results with the droplet model which have been found in simulations of three-dimensional Ising spin glasses.