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 Jeff and effective field Heff of each sample are measured by a numerical renormalization-group method, and their sample-to-sample fluctuations σJ and σH are estimated for various sizes L and fields H. As found in the Migdal-Kadanoff spin glass, σJ and σH 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 σJ drops to zero in the limit L/l(H)→∞. These results indicate the absence of spin glass phase even in an infinitesimal field