On the mixed even-spin Sherrington–Kirkpatrick model with ferromagnetic interaction

Wei-Kuo Chen

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 1, page 63-83
  • ISSN: 0246-0203

Abstract

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We study a spin system with both mixed even-spin Sherrington–Kirkpatrick (SK) couplings and Curie–Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the free energy of the SK model with a change in the external field. (ii) In the presence of a centered Gaussian external field, the positivity of the overlap and the extended Ghirlanda–Guerra identities hold on a dense subset of the temperature parameters. (iii) We establish a general inequality between the magnetization and overlap. (iv) We construct a temperature region in which the magnetization can be quantitatively controlled and deduce different senses of convergence for the magnetization depending on whether the external field is present or not. Our approach is based on techniques from the study of the CW and SK models and results in convex analysis.

How to cite

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Chen, Wei-Kuo. "On the mixed even-spin Sherrington–Kirkpatrick model with ferromagnetic interaction." Annales de l'I.H.P. Probabilités et statistiques 50.1 (2014): 63-83. <http://eudml.org/doc/272027>.

@article{Chen2014,
abstract = {We study a spin system with both mixed even-spin Sherrington–Kirkpatrick (SK) couplings and Curie–Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the free energy of the SK model with a change in the external field. (ii) In the presence of a centered Gaussian external field, the positivity of the overlap and the extended Ghirlanda–Guerra identities hold on a dense subset of the temperature parameters. (iii) We establish a general inequality between the magnetization and overlap. (iv) We construct a temperature region in which the magnetization can be quantitatively controlled and deduce different senses of convergence for the magnetization depending on whether the external field is present or not. Our approach is based on techniques from the study of the CW and SK models and results in convex analysis.},
author = {Chen, Wei-Kuo},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {ferromagnetic interaction; Ghirlanda–Guerra identities; Parisi formula; Sherrington-Kirkpatrick model; ultrametricity; Ghirlanda-Guerra identities},
language = {eng},
number = {1},
pages = {63-83},
publisher = {Gauthier-Villars},
title = {On the mixed even-spin Sherrington–Kirkpatrick model with ferromagnetic interaction},
url = {http://eudml.org/doc/272027},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Chen, Wei-Kuo
TI - On the mixed even-spin Sherrington–Kirkpatrick model with ferromagnetic interaction
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 1
SP - 63
EP - 83
AB - We study a spin system with both mixed even-spin Sherrington–Kirkpatrick (SK) couplings and Curie–Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the free energy of the SK model with a change in the external field. (ii) In the presence of a centered Gaussian external field, the positivity of the overlap and the extended Ghirlanda–Guerra identities hold on a dense subset of the temperature parameters. (iii) We establish a general inequality between the magnetization and overlap. (iv) We construct a temperature region in which the magnetization can be quantitatively controlled and deduce different senses of convergence for the magnetization depending on whether the external field is present or not. Our approach is based on techniques from the study of the CW and SK models and results in convex analysis.
LA - eng
KW - ferromagnetic interaction; Ghirlanda–Guerra identities; Parisi formula; Sherrington-Kirkpatrick model; ultrametricity; Ghirlanda-Guerra identities
UR - http://eudml.org/doc/272027
ER -

References

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