Spin glasses on the hypercube

L. A. Fernández, V. Martin-Mayor, G. Parisi, and B. Seoane
Phys. Rev. B 81, 134403 – Published 2 April 2010

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 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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
15 More
  • Received 30 November 2009

DOI:https://doi.org/10.1103/PhysRevB.81.134403

©2010 American Physical Society

Authors & Affiliations

L. A. Fernández1,2, V. Martin-Mayor1,2, G. Parisi3, and B. Seoane1,2

  • 1Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
  • 2Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Zaragoza, Spain
  • 3Dipartimento di Fisica, INFM-CNR (SMC), Università di Roma “La Sapienza,” 00185 Roma, Italy

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 81, Iss. 13 — 1 April 2010

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×