FREE ENERGY OF A DILUTED SPIN GLASS MODEL WITH QUADRATIC HAMILTONIAN

• 成果类型: Article
• 署名作者: Biswas, Ratul; Chen, Wei-kuo; Sen, Arnab
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1597
• 发表日期: 2023
• 页码: 359-395
• 关键词: Bounds

摘要

We study a diluted mean-field spin glass model with a quadratic Hamil-tonian. Our main result establishes the limiting free energy in terms of an in-tegral of a family of random variables that are the weak limits of the quenched variances of the spins in the system with varying edge connectivity. The key ingredient in our argument is played by the identification of these random variables as the unique solution to a recursive distributional equation. Our re-sults in particular provide the first example of the diluted Shcherbina-Tirozzi model, whose limiting free energy can be derived at any inverse temperature and external field.