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With the help of the replica exchange Monte Carlo method and the improvedMonte Carlo renormalization-group scheme, we investigate over a wide area inthe phase diagram of the Gaussian random field Ising model on the simple cubiclattice. We found that the phase transition at a weak random field belongs tothe same universality class as the zero-temperature phase transition. We alsopresent a possible scenario for the replica symmetry breaking transition.Comment: 4 pages, revtex, 6 figures. Final version to appear in PRB(Brief  Report

Phase diagram of the three-dimensional Gaussian random field Ising model: A Monte Carlo renormalization-group study