The percolation signature of the spin glass transition

J. MacHta, Charles Newman, D. L. Stein

Research output: Contribution to journalArticle

Abstract

Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering-both in short-range (EA) and infinite-range (SK) models-within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the ±J EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of two percolating clusters of unequal densities.

Original languageEnglish (US)
Pages (from-to)113-128
Number of pages16
JournalJournal of Statistical Physics
Volume130
Issue number1
DOIs
StatePublished - Jan 2008

Fingerprint

Glass Transition
Spin Glass
spin glass
Signature
signatures
Replica
replicas
Ising
Ferromagnet
Graphical Representation
Unequal
Range of data
Three-dimension
Numerical Study
Model
occurrences

Keywords

  • Cluster algorithms
  • Fortuin-Kasteleyn
  • Graphical representations
  • Ising spin glass
  • Percolation

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

The percolation signature of the spin glass transition. / MacHta, J.; Newman, Charles; Stein, D. L.

In: Journal of Statistical Physics, Vol. 130, No. 1, 01.2008, p. 113-128.

Research output: Contribution to journalArticle

MacHta, J. ; Newman, Charles ; Stein, D. L. / The percolation signature of the spin glass transition. In: Journal of Statistical Physics. 2008 ; Vol. 130, No. 1. pp. 113-128.
@article{400a113dfb024cde930e2b0881deb105,
title = "The percolation signature of the spin glass transition",
abstract = "Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering-both in short-range (EA) and infinite-range (SK) models-within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the ±J EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of two percolating clusters of unequal densities.",
keywords = "Cluster algorithms, Fortuin-Kasteleyn, Graphical representations, Ising spin glass, Percolation",
author = "J. MacHta and Charles Newman and Stein, {D. L.}",
year = "2008",
month = "1",
doi = "10.1007/s10955-007-9446-2",
language = "English (US)",
volume = "130",
pages = "113--128",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - The percolation signature of the spin glass transition

AU - MacHta, J.

AU - Newman, Charles

AU - Stein, D. L.

PY - 2008/1

Y1 - 2008/1

N2 - Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering-both in short-range (EA) and infinite-range (SK) models-within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the ±J EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of two percolating clusters of unequal densities.

AB - Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering-both in short-range (EA) and infinite-range (SK) models-within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the ±J EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of two percolating clusters of unequal densities.

KW - Cluster algorithms

KW - Fortuin-Kasteleyn

KW - Graphical representations

KW - Ising spin glass

KW - Percolation

UR - http://www.scopus.com/inward/record.url?scp=36749006155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749006155&partnerID=8YFLogxK

U2 - 10.1007/s10955-007-9446-2

DO - 10.1007/s10955-007-9446-2

M3 - Article

AN - SCOPUS:36749006155

VL - 130

SP - 113

EP - 128

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -