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

We study the four dimensional (4D) $\pm J$ Ising spin glass in a magnetic field by using the simulated tempering method recently introduced by Marinari and Parisi. We compute numerically the first four moments of the order parameter probability distribution $P(q)$. We find a finite cusp in the spin-glass susceptibility and strong tendency to paramagnetic ordering at low temperatures. Assuming a well defined transition we are able to bound its critical temperature.