Numerical study of the Sherrington-Kirkpatrick model in a magnetic field.

We study numerically the Sherrington-Kirkpatrick model as a function of the magnetic field h, with fixed temperature T=0.6T(c). We investigate the finite size scaling behavior of several quantities, such as the spin-glass susceptibility, searching for numerical evidences of the transition on the de Almeida-Thouless line. We find strong corrections to scaling which make difficult to locate the transition point. This shows, in a simple case, the extreme difficulties of spin-glass simulations in a nonzero magnetic field. Next, we study various sum rules (consequences of stochastic stability) involving overlaps between three and four replicas, which appear to be numerically well satisfied, and in a nontrivial way. Finally, we present data on P(q) for a large lattice size (N=3200) at low temperature T=0.4T(c), where the shape predicted by the replica symmetry breaking solution of the model for a nonzero magnetic field is visible.