Corrections to scaling in the droplet picture of spin glasses

TL;DR

This paper proposes a correction to the droplet energy scaling in spin glasses, adding a term that aligns numerical data across dimensions with the droplet model.

Contribution

It introduces a scaling correction to the droplet energy formula, improving the compatibility of numerical results with the droplet theory.

Findings

Scaling correction $L^{-}$ reconciles data with the droplet model

Numerical data in 2D, 3D, and 4D are consistent with the modified scaling

Supports the validity of the droplet picture in spin glasses

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 argued 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. With this simple modification all equilibrium numerical data on Ising spin glasses in two, three and four dimensions becomes compatible with the droplet model.