Spin Glasses on the Hypercube

Details Spin Glasses on the Hypercube Spin Glasses on the Hypercube

2009-11-24

arxiv.org/abs/0911.4667v1

Phys. Rev. B 81, 134403 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages, 22 figures

Scientific paper

10.1103/PhysRevB.81.134403

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 non trivial problem of generating these lattices. Afterwards, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are: (i) the dynamics is ruled by an infinite number of time-sectors, (ii) the aging dynamics consists on the growth of coherent domains with a non vanishing surface-volume ratio, and (iii) the propagator in Fourier space follows the p^4 law. We study as well finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.

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