Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model

TL;DR

This paper proves central limit theorems for macroscopic observables, especially the energy density, in the high temperature Sherrington-Kirkpatrick model using a novel combination of cavity and Stein's methods.

Contribution

It introduces a quenched CLT for the energy density with external field, extending previous results by integrating cavity and Stein's techniques.

Findings

Established quenched CLT for energy density with external field

Extended previous CLT results to more general conditions

Combined cavity method with Stein's method effectively

Abstract

In this paper we consider central limit theorems for various macroscopic observables in the high temperature region of the Sherrington-Kirkpatrick spin glass model. With a particular focus on obtaining a quenched central limit theorem for the energy density of the system with non-zero external field, we show how to combine the mean field cavity method with Stein's method in the quenched regime. The result for the energy density extends the corresponding result of Comets-Neveu.