铁磁性三维<strong>Ising</strong>模型精确解及时间的自发产生

doi:10.11900/0412.1961.2022.00486

金属学报

2023, Vol. 59

Issue (4): 489-501 DOI: 10.11900/0412.1961.2022.00486

综述

本期目录 | 过刊浏览

铁磁性三维Ising模型精确解及时间的自发产生

张志东(

)

中国科学院金属研究所沈阳材料科学国家研究中心沈阳 110016

Exact Solution of Ferromagnetic Three-Dimensional (3D) Ising Model and Spontaneous Emerge of Time

ZHANG Zhidong(

)

Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China

引用本文:

张志东. 铁磁性三维Ising模型精确解及时间的自发产生[J]. 金属学报, 2023, 59(4): 489-501.
Zhidong ZHANG. Exact Solution of Ferromagnetic Three-Dimensional (3D) Ising Model and Spontaneous Emerge of Time[J]. Acta Metall Sin, 2023, 59(4): 489-501.

全文: PDF(1224 KB) HTML

摘要:

本文综述在三维Ising模型精确解方面取得的研究进展。首先介绍作者构建的拓扑量子统计物理学，包括时间平均、Jordan-von Neumann-Wigner框架、拓扑结构对热力学性质的贡献等学术思想。然后介绍用Clifford代数方法和Riemann-Hilbert问题的方法证明作者提出的两个猜想，证明在两个猜想基础上推定的三维Ising精确解的正确性。在此基础上，探究了时间的本源，得出三维多体相互作用体系中粒子(自旋)间相互作用自发产生时间的结论。

关键词 ： Ising模型, 精确解, 拓扑量子统计, 时间, 多体相互作用

Abstract：

This article reviews recent advances in the exact solution of ferromagnetic three-dimensional (3D) Ising model. First, the topological quantum statistic mechanism was introduced, which includes the time average, Jordan-von Neumann-Wigner framework, and the contribution of topological structures to thermodynamic properties of the system. Then, the Clifford algebra approach and the method of the Riemann-Hilbert problem were introduced to prove Zhang's two conjectures for the exact solution of the ferromagnetic 3D Ising model. The proof process verifies the correctness of the Zhang's exact solution for the ferromagnetic 3D Ising model. Based on these progresses, the origin of time was investigated and driven to the conclusion that in 3D many-body interacting particle (or spin) systems, time emerges spontaneously from many-body interactions.

Key words： Ising model exact solution topological quantum statistic time many-body interaction

收稿日期: 2022-10-08

ZTFLH:

O414.21

基金资助:国家自然科学基金项目(52031014)

通讯作者: 张志东，zdzhang@imr.ac.cn，主要从事磁性和磁性材料、凝聚态物理、统计物理研究

Corresponding author: ZHANG Zhidong, professor, Tel: (024)23971859, E-mail: zdzhang@imr.ac.cn

作者简介: 张志东，男，1963年生，研究员，博士

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https://www.ams.org.cn/CN/10.11900/0412.1961.2022.00486 或 https://www.ams.org.cn/CN/Y2023/V59/I4/489

图1 与纽结γ的晶格点相连接的转移矩阵 V3 中辫子的3条举例[21]

图2 拓扑结构的交叉与Ising自旋指向(自旋向上、自旋向下)、自旋数值(+1或者-1)之间的映射关系[22]

图3 具有随机交叉分布的二维纽结与一个二维Ising模型之间的映射[22]

图4 一个辫子与一个自旋链的映射关系[22]

图5 三维Ising模型一个晶格单胞示意图[22]

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