Fluctuations of the free energy in p-spin SK models on two scales

TL;DR

This paper extends the understanding of free energy fluctuations in p-spin SK models across a broader temperature range, identifying the main fluctuation source and establishing a new CLT for deviations around it.

Contribution

It improves previous CLT results by covering the full temperature regime where quenched and annealed free energies match, and pinpoints the primary fluctuation source.

Findings

Extended CLT to entire temperature regime

Identified coupling-dependent term as main fluctuation source

Established CLT for free energy deviations around this term

Abstract

20 years ago, Bovier, Kurkova, and L\"owe [5] proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick model of spin glasses at high temperatures. In this paper we improve their results in two ways. First, we extend the range of temperatures to cover the entire regime where the quenched and annealed free energies are known to coincide. Second, we identify the main source of the fluctuations as a purely coupling dependent term, and we show a further CLT for the deviation of the free energy around this random object.