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 $O((\log N)^2+N^{ 1-\alpha}).$
Categories: math.PR