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

We study numerically the region above the critical temperature of the four-dimensional random field Ising model. Using a cluster dynamic we measure the connected and disconnected magnetic susceptibility and the connected and disconnected overlap susceptibility. We use a bimodal distribution of the field with h(R) = 0.35T for all temperatures and a lattice size L = 16. Through a least-square fit we determine the critical temperature at which the two susceptibilities diverge. We also determine the critical exponents gamma and <(gamma)over bar>. We find that the magnetic susceptibility and the overlap susceptibility diverge at two different temperatures. This is coherent with the existence of a glassy phase above T-c. Accordingly with other simulations we find <(gamma)over bar> = 2 gamma. In this case we have a scaling theory with two independent critical exponents.