Magnetic exponents of two-dimensional Ising spin glasses

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 δ≈1.30±0.02 using lattice sizes up to 80×80; this is compatible with the droplet model prediction, δ=1.282. The reason for previous disagreements stems from the need to analyze both singular and analytic contributions in the low-field regime.