The magnetic critical properties of two-dimensional Ising spin glasses are controversial. Using an exact ground-state determination, we extract the properties of clusters flipped when a uniform field is increased continuously. We show that these clusters have many holes but otherwise have statistical properties similar to those of zero-field droplets. A detailed analysis gives for the magnetization exponent $\delta \approx 1.30\pm 0.02$ using lattice sizes up to $80\times 80$; this is compatible with the droplet model prediction, $\delta =1.282$. The reason for previous disagreements stems from the need to analyze both singular and analytic contributions in the low-field regime.

• Received 13 July 2007

DOI:https://doi.org/10.1103/PhysRevB.76.060405