Absence of spin glass phase in the Edwards-Anderson Ising spin glass in magnetic field

The presence (or absence) of spin glass phase in uniform magnetic field is studied in the three and four dimensional Edwards-Anderson Ising spin glass. Effective coupling J_eff and effective field H_eff of each sample are measured by a numerical renormalization-group method, and their sample-to-sample fluctuations σ_J and σ_H are estimated for various sizes L and fields H. As found in the Migdal-Kadanoff spin glass, σ_J and σ_H are scaled as a function of L / ℓ (H), where ℓ (H) = H^{- 1 / ζ} is the so-called overlap length. Furthermore, our data show that the scaling function of σ_J drops to zero in the limit L / ℓ (H) → ∞. These results indicate the absence of spin glass phase even in an infinitesimal field.