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

• 成果类型: Article
• 署名作者: Bovier, Anton; Schertzer, Adrien
• 署名单位: University of Bonn
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01296-y
• 发表日期: 2024
• 页码: 771-810
• 关键词: solvable model; glasses

摘要

20 years ago, Bovier, Kurkova, and L & ouml;we (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.