Large deviations, Guerra's and ASS schemes, and the Parisi hypothesis

We investigate the problem of computing lim(N -> infinity) 1/aN log EZ(N)(a) for any value of a, where Z(N) is the partition function of the celebrated Sherrington-Kirkpatrick (SK) model, or of some of its natural generalizations. This is a natural "large deviation" problem. Its study helps to get a fresh look at some of the recent ideas introduced in the area, and raises a number of natural questions. We provide a complete solution for a >= 0.