Spin Glasses on the Hypercube

TL;DR

This paper introduces a mean field model for spin glasses on a hypercube, analyzing their dynamics and finite size effects, revealing complex aging behavior and a p^4 propagator law.

Contribution

It develops a new hypercube-based mean field model for spin glasses and investigates their nonequilibrium dynamics, uncovering multiple time sectors and domain growth phenomena.

Findings

Dynamics governed by infinite time sectors

Aging involves growth of coherent domains with non-zero surface-volume ratio

Fourier space propagator follows p^4 law

Abstract

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.