Abstract
We study the problem of disorder chaos in the spherical mean-field model. It concerns the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters. The prediction states that if the disorders in the Hamiltonians are slightly decoupled, then the overlap will be concentrated near a constant value. Following Guerra’s replica symmetry breaking scheme, we establish this at the levels of the free energy and the Gibbs measure.
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References
Chatterjee, S.: Disorder chaos and multiple valleys in spin glasses (2009). Preprint available at arXiv:0907.3381
Chen, W.-K.: Disorder chaos in the Sherrington–Kirkpatrick model with external field. Ann. Probab. 41(5), 3345–3391 (2013)
Chen, W.-K.: The Aizenman–Sims–Starr scheme and Parisi formula for mixed \(p\)-spin spherical models. Electron. J. Probab. 18(94), 1–14 (2013)
Chen, W.-K.: Chaos in the mixed even-spin models. Comm. Math. Phys. 328(3), 867–901 (2014)
Chen, W.-K.: Variational representations for the Parisi functional and the two-dimensional Guerra–Talagrand bound (2015). Preprint available at arXiv:1501.06635
Chen, W.-K., Panchenko, D.: An approach to chaos in some mixed \(p\)-spin models. Probab. Theory Rel. Fields 157(1–2), 389–404 (2013)
Panchenko, D.: A note on Talagrand’s positivity principle. Electron. Comm. Probab. 12, 401–410 (2007)
Panchenko, D.: Chaos in temperature in generic \(2p\)-spin models (2015). Preprint available at arXiv:1502.03801
Panchenko, D., Talagrand, M.: On the overlap in the multiple spherical SK models. Ann. Probab. 35(6), 2321–2355 (2007)
Rizzo, T.: Spin glasses: statics and dynamics: summer school, Paris 2007. Progr. Probab. 62, 143–157 (2009)
Talagrand, M.: Free energy of the spherical mean field model. Probab. Theory Rel. Fields 134(3), 339–382 (2006)
Talagrand, M.: Mean field models for spin glasses. Ergebnisse der Mathematik und ihrer Grenzgebiete 3 Folge. A Series of Modern Surveys in Mathematics, vol. 55, Springer, Berlin (2011)
Acknowledgments
The authors thank anonymous referees for the careful reading and giving several suggestions regarding the presentation of the paper. Wei-Kuo Chen and Yuan-Chung Sheu also thank CMMSC(NCTU, Taiwan) and NCTS(Taiwan) for the partial supports during the early stage of the project.
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Chen, WK., Hsieh, HW., Hwang, CR. et al. Disorder Chaos in the Spherical Mean-Field Model. J Stat Phys 160, 417–429 (2015). https://doi.org/10.1007/s10955-015-1264-3
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DOI: https://doi.org/10.1007/s10955-015-1264-3