Spin glasses on the hypercube

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 p(4) law. We study as well the finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.