Some rigorous results on the Sherrington-Kirkpatrick spin glass model

We prove that in the high temperature regime (T/J>1) the deviation of the total free energy of the Sherrington-Kirkpatrick (S-K) spin glass model from the easily computed log Av(Z_N({J})) converges in distribution, asN , to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.Dedicated to Walter Thirring on his 60^th birthdayResearch supported in part by the NSF grant PHY-8605164. Present address: Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012, USAResearch supported in part by the NSF grant DMR 86-12369On leave from Institut des Hautes Etudes Scientifiques, Bures-Sur-Yvette, France