Scaling analysis of domain-wall free energy in the Edwards-Anderson Ising spin glass in a magnetic field

The stability of the spin-glass phase against a magnetic field is studied in the three- and four-dimensional Edwards-Anderson Ising spin glasses. Effective couplings J(eff) and effective fields H(eff) associated with length scale L are measured by a numerical domain-wall renormalization-group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H --> 0 but remains finite for any nonzero H, implying that the spin-glass phase is absent even in an infinitesimal field. These results are well consistent with the droplet theory for short-range spin glasses.