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.

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协方差矩阵及其特征值分布函数在高温间的及其限制的极限，以及TAP方程。 该提案还包括一个在稀释的自旋玻璃模型中计算自由能的问题。旋转玻璃的严格理论将对许多领域和学科产生广泛的科学影响，包括物理，凝结物质理论，概率和分析。 例如，了解超级图片最终可能会导致对广泛用于物理学的著名Parsi技巧的理解。 成功可能有助于在其他自旋玻璃模型和更多具有兴趣的物理系统（例如量子自旋玻璃杯）中取得进展。