Fluctuations of the free energy in the mixed p-spin models with external field

• 成果类型: Article
• 署名作者: Chen, Wei-Kuo; Dey, Partha; Panchenko, Dmitry
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Illinois System; University of Illinois Urbana-Champaign; University of Toronto
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0705-5
• 发表日期: 2017
• 页码: 41-53
• 关键词: disorder chaos

摘要

We show that the free energy in the mixed p-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar, inequality. This complements the result of Chatterjee who showed that the free energy superconcentrates when there is no external field. For models without odd p-spin interactions for , we prove the central limit theorem for the free energy at any temperature and give an explicit formula for the limiting variance. Although we only deal with the case of Ising spins, all our results can be extended to the spherical models as well.