Spin Glasses on the Hypercube

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.

14 pages, 22 figures

References in corpus (8)

• The critical behavior of three-dimensional Ising spin glass models
• An in-depth view of the microscopic dynamics of Ising spin glasses at fixed temperature
• Diluted one-dimensional spin glasses with power law decaying interactions
• Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
• Full Aging in Spin Glasses
• Dynamical ultrametricity in the critical trap model
• Mean field theory of spin glasses: statics and dynamics
• On the high density behavior of Hamming codes with fixed minimum distance

Cited by in corpus (8)

• Nature of the spin-glass phase at experimental length scales
• The correspondence between long-range and short-range spin glasses
• Aging in coarsening diluted ferromagnets
• Testing statics-dynamics equivalence at the spin-glass transition in three dimensions
• Dynamic Variational Study of Chaos: Spin Glasses in Three Dimensions
• Kinked Entropy and Discontinuous Microcanonical Spontaneous Symmetry Breaking
• Spatial correlation functions and dynamical exponents in very large samples of 4D spin glasses
• Deepening the knowledge of Spin Glasses: Metastate, Off-equilibrium phenomena and Temperature Chaos