Energetics of clusters in the two-dimensional Ising spin glass

TL;DR

This paper investigates the properties of low-energy excitations in 2D Ising spin glasses to clarify scaling corrections and estimate the stiffness exponent, finding results consistent with domain wall calculations.

Contribution

It provides a numerical analysis of local excitations in 2D Ising spin glasses, addressing scaling corrections and estimating the stiffness exponent.

Findings

No clear evidence of corrections to scaling

Stiffness exponent aligns with domain wall calculations

Supports the droplet picture of spin glasses

Abstract

We study numerically the properties of local low-energy excitations in the two-dimensional Ising spin glass. Given the ground state, we determine the lowest-lying connected cluster of flipped spins containing one given spin, either with a fixed volume, or with a volume constrained to lie in a certain range. Our aim is to understand corrections to the scaling predicted by the droplet picture of spin glasses and to resolve contradictory results reported in the literature for the stiffness exponent. We find no clear trace of corrections to scaling, and the obtained stiffness exponent is in relatively good agreement with standard domain wall calculations.