Tempering simulations in the four dimensional ±J Ising spin glass in a magnetic field

We study the four dimensional (4D) ±J Ising spin glass in a magnetic field with the simulated tempering algorithm recently introduced by Marinari and Parisi. We compute numerically the order parameter function P(q) and analyze the temperature dependence of the first four cumulants of the distribution. We discuss the evidence in favor of the existence of a phase transition in a field. Assuming a well defined transition we are able to bound its critical temperature.