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تسجيل مستخدم جديدOrder of Fluctuations of the Free Energy in the SK Model at Critical Temperature
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We present an elementary approach to the order of fluctuations for the free energy in the Sherrington-Kirkpatrick mean field spin glass model at and near the critical temperature. It is proved that at the critical temperature the variance of the free energy is of $O((log N)^2).$ In addition, we show that if one approaches the critical temperature from the low temperature regime at the rate $O(N^{-alpha})$ for some $alpha>0,$ then the variance is of $O((log N)^2+N^{1-alpha}).$
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