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© 2010 The American Physical Society. We thank Federico Ricci-Tersenghi for discussions. Computations have been carried out in PC clusters at BIFI and DFTI-UCM. We have been partly supported by MICINN, Spain through Research Contracts No. FIS2006-08533 and No. FIS2009-12648-C03 and by UCM-Banco de Santander through Grant No. GR58/08. B.S. was supported by the FPU program Spain., We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the nontrivial problem of generating these lattices. Afterward, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are the following: i the dynamics is ruled by an infinite number of time sectors, ii the aging dynamics consists of the growth of coherent domains with a nonvanishing surface-volume ratio, and iii the propagator in Fourier space follows the p4 law. We study as well the finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well., Ministerio de Ciencia e Innovación (MICINN), UCM-Banco de Santander, FPU program, Spain, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2010 The American Physical Society. We thank Federico Ricci-Tersenghi for discussions. Computations have been carried out in PC clusters at BIFI and DFTI-UCM. We have been partly supported by MICINN, Spain through Research Contracts No. FIS2006-08533 and No. FIS2009-12648-C03 and by UCM-Banco de Santander through Grant No. GR58/08. B.S. was supported by the FPU program Spain., We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the nontrivial problem of generating these lattices. Afterward, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are the following: i the dynamics is ruled by an infinite number of time sectors, ii the aging dynamics consists of the growth of coherent domains with a nonvanishing surface-volume ratio, and iii the propagator in Fourier space follows the p4 law. We study as well the finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well., Ministerio de Ciencia e Innovación (MICINN), UCM-Banco de Santander, FPU program, Spain, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub