Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Replica Symmetry Breaking and Exponential Inequalities for the Sherrington- Kirkpatrick Model

Michel Talagrand
The Annals of Probability
Vol. 28, No. 3 (Jul., 2000), pp. 1018-1062
Stable URL: http://www.jstor.org/stable/2652978
Page Count: 45
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Replica Symmetry Breaking and Exponential Inequalities for the Sherrington- Kirkpatrick Model
Preview not available

Abstract

We provide an extremely accurate picture of the Sherrington-Kirkpatrick model in three cases: for high temperature, for large external field and for any temperature greater than or equal to 1 and sufficiently small external field. We describe the system at the level of the central limit theorem, or as physicists would say, at the level of fluctuations around the mean field. We also obtain much more detailed information, in the form of exponential inequalities that express a uniform control over higher order moments. We give a complete, rigorous proof that at the generic point of the predicted low temperature region there is "replica symmetry breaking," in the sense that the system is unstable with respect to an infinitesimal coupling between two replicas.

Page Thumbnails

  • Thumbnail: Page 
1018
    1018
  • Thumbnail: Page 
1019
    1019
  • Thumbnail: Page 
1020
    1020
  • Thumbnail: Page 
1021
    1021
  • Thumbnail: Page 
1022
    1022
  • Thumbnail: Page 
1023
    1023
  • Thumbnail: Page 
1024
    1024
  • Thumbnail: Page 
1025
    1025
  • Thumbnail: Page 
1026
    1026
  • Thumbnail: Page 
1027
    1027
  • Thumbnail: Page 
1028
    1028
  • Thumbnail: Page 
1029
    1029
  • Thumbnail: Page 
1030
    1030
  • Thumbnail: Page 
1031
    1031
  • Thumbnail: Page 
1032
    1032
  • Thumbnail: Page 
1033
    1033
  • Thumbnail: Page 
1034
    1034
  • Thumbnail: Page 
1035
    1035
  • Thumbnail: Page 
1036
    1036
  • Thumbnail: Page 
1037
    1037
  • Thumbnail: Page 
1038
    1038
  • Thumbnail: Page 
1039
    1039
  • Thumbnail: Page 
1040
    1040
  • Thumbnail: Page 
1041
    1041
  • Thumbnail: Page 
1042
    1042
  • Thumbnail: Page 
1043
    1043
  • Thumbnail: Page 
1044
    1044
  • Thumbnail: Page 
1045
    1045
  • Thumbnail: Page 
1046
    1046
  • Thumbnail: Page 
1047
    1047
  • Thumbnail: Page 
1048
    1048
  • Thumbnail: Page 
1049
    1049
  • Thumbnail: Page 
1050
    1050
  • Thumbnail: Page 
1051
    1051
  • Thumbnail: Page 
1052
    1052
  • Thumbnail: Page 
1053
    1053
  • Thumbnail: Page 
1054
    1054
  • Thumbnail: Page 
1055
    1055
  • Thumbnail: Page 
1056
    1056
  • Thumbnail: Page 
1057
    1057
  • Thumbnail: Page 
1058
    1058
  • Thumbnail: Page 
1059
    1059
  • Thumbnail: Page 
1060
    1060
  • Thumbnail: Page 
1061
    1061
  • Thumbnail: Page 
1062
    1062