Exponential Control of Overlap in the Replica Method for p-Spin Sherrington-Kirkpatrick Model

摘要

In Talagrand (J. Stat. Phys. 126(4–5):837–894, 2007) the large deviations limit lim_N®¥(Na)-1logmathbb EZ_Nalim_{Ntoinfty}(Na)^{-1}log mathbb {E}Z_{N}^{a} for the moments of the partition function Z _N in the Sherrington-Kirkpatrick model (Sherrington and Kirkpatrick in Phys. Rev. Lett. 35:1792–1796, 1972) was computed for all real a≥0. For a≥1 this result extends the classical physicist’s replica method that corresponds to integer values of a. We give a new proof for a≥1 in the case of the pure p-spin SK model that provides a strong exponential control of the overlap.