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

Abstract 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.