Spin Glass Models

旋转玻璃模型

• 批准号: 0504108
• 负责人: Dmitriy Panchenko
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504108&HistoricalAwards=false
• 关键词: Spin; Glass; Models

The proposed research concerns spin glass models and addresses important questions related to the Sherringon-Kirkpatrick and the generalized Sherrington-Kirkpatrick models that include characterization of replica symmetric region and phase transitions, replica symmetry breaking, uniqueness of Parsi measure and its properties, strong Ghirlanda-Guerra identities, chaos and ultrametricity conjectures, boundedness of the operator norm of the covariance matrix and the limit of its eigenvalue distribution function in the high temperature ragion, and the TAP equations. The proposal also includes a question of computing the free energy in the diluted spin glass model.The rigorous theory of spin glasses will have broad scientific impact on a number of areas and disciplines, including physics, condensed matter theory, probability and analysis. For example, understanding the ultrametric picture could eventually lead to understanding of the famous Parsi trick which is widely used in physics. Success will probably help in making progress in other spin glass models and more physical systems of great interest such as quantum spin glasses.

本论文的主要研究内容是自旋玻璃模型，并解决了与Sherringon-Kirkpatrick模型和广义Sherrington-Kirkpatrick模型相关的重要问题，包括副本对称区域和相变的表征，副本对称破缺，Parsi测度的唯一性及其性质，强Ghirlanda-Guerra恒等式，混沌和超度量结构，协方差矩阵的算子范数的有界性及其特征值分布函数在高温区的极限，以及TAP方程。 这项建议亦包括计算稀释自旋玻璃模型中的自由能的问题。自旋玻璃的严谨理论将对多个范畴和学科产生广泛的科学影响，包括物理学、凝聚态理论、概率论和分析。 例如，理解超度规图像可能最终导致理解在物理学中广泛使用的著名的帕西技巧。 这一成功可能有助于在其他自旋玻璃模型和更令人感兴趣的物理系统（如量子自旋玻璃）方面取得进展。