Abstract
Abstract20 years ago, Bovier, Kurkova, and Löwe (Ann Probab 30(2):605–651, 2002) 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.
Funder
Deutsche Forschungsgemeinschaft
Rheinische Friedrich-Wilhelms-Universität Bonn
Publisher
Springer Science and Business Media LLC
Reference15 articles.
1. Aizenman, M., Lebowitz, J., Ruelle, D.: Some rigorous results on the Sherrington–Kirkpatrick spin glass model. Commun. Math. Phys. 112(1), 3–20 (1987)
2. Baik, J.B., Lee, J.O.: Fluctuations of the free energy of the spherical Sherrington–Kirkpatrick model. J. Stat. Phys. 165, 185–224 (2016)
3. Banerjee, D., Belius, D.: Fluctuations of the free energy of the mixed $$p$$-spin mean field spin glass model (2021). arXiv preprint arXiv:2108.03109
4. Cambridge Series in Statistical and Probabilistic Mathematics;A Bovier,2006
5. Bovier, A., Kurkova, I., Löwe, M.: Fluctuations of the free energy in the REM and the p-spin SK models. Ann. Probab. 30(2), 605–651 (2002)