Phase structure of the three-dimensional Edwards-Anderson spin glass

We characterize numerically the properties of the phase transition of the t hree-dimensional Ising spin glass with Gaussian couplings and of the low-te mperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap- overlap correlation functions. We find a clear agreement with off-equilibri um results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three-dimensional spin glasses. [S0163-1829(98)03141-5].