Some Rigorous Results on the Sherrington-Kirkpatrick Model of Spin Glasses

Abstract. 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 logAv(Z N ({βJ})) converges in distribution, as ΛΓ-KX), to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained