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We study numerically the region above the critical temperature of the fourdimensional Random Field Ising Model. Using a cluster dynamic we measure theconnected and disconnected magnetic susceptibility and the connected anddisconnected overlap susceptibility. We use a bimodal distribution of the fieldwith $ h_R=0.35T $ for all temperatures and a lattice size L=16. Through aleast-square fit we determine the critical exponents $ \gamma $ and $\bar{\gamma} $. We find the magnetic susceptibility and the overlapsusceptibility diverge at two different temperatures. This is coherent with theexistence of a glassy phase above $ T_c $. Accordingly with other simulationswe find $ \bar{\gamma}=2\gamma $. In this case we have a scaling theory withtwo indipendet critical exponentsComment: 10 pages, 2 figures, Late

Numerical study of the transition of the four-dimensional random field Ising model