MATHEMATICAL STRUCTURE AND THE CONJECTURED EXACT SOLUTION OF THREEDIMENSIONAL (3D) ISING MODEL
文献类型：期刊论文
| 作者 | Zhang Zhidong |
| 刊名 | ACTA METALLURGICA SINICA
 |
| 出版日期 | 2016-10-01 |
| 卷号 | 52期号:10页码:1311-1325 |
| ISSN号 | 0412-1961 |
| 关键词 | Ising model mathematical structure exact solution topological property algebraic property geometric property |
| DOI | 10.11900/0412.1961.2016.00336 |
| 通讯作者 | Zhang Zhidong(zdzhang@imr.ac.cn) |
| 英文摘要 | In this article, the history of study on Ising model was first reviewed briefly, including a brief introduction of Ising model, the advances in the study of two-dimensional (2D) and three-dimensional (3D) Ising models, with a special interest in the exact solution of the 2D Ising model. Then two conjectures and putative exact solution of the 3D Ising model were introduced, and the mathematical structure of the 3D Ising model was investigated from the aspects of topology, algebra and geometry. The transfer matrices of the 3D Ising model, the knot theory in the topology, the relations between the Yang-Baxter equations and the tetrahedron equations were analysized. The non-local effect in the 3D Ising model, the relation between quantum field theory and gauge theory, the physical significance of weight factors, the singularity and the topological phase transition at/near infinite temperature in the 3D Ising model were also discussed. Finally, it was pointed out that some approximation techniques (for examples, low-temperature expansions, high-temperature expansions, renormalization group and Monte Carlo simulations) have disadvantages for studying the 3D Ising model. |
| 资助项目 | National Natural Science Foundation of China[51331006] ; National Natural Science Foundation of China[51590883] |
| WOS研究方向 | Metallurgy & Metallurgical Engineering |
| 语种 | 英语 |
| 出版者 | SCIENCE PRESS |
| WOS记录号 | WOS:000390080900015 |
| 资助机构 | National Natural Science Foundation of China |
| 源URL | [http://ir.imr.ac.cn/handle/321006/123351]  |
| 专题 | 金属研究所_中国科学院金属研究所 |
| 通讯作者 | Zhang Zhidong |
| 作者单位 | Chinese Acad Sci, Inst Met Res, Shenyang Natl Lab Mat Sci, Shenyang 110016, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhang Zhidong. MATHEMATICAL STRUCTURE AND THE CONJECTURED EXACT SOLUTION OF THREEDIMENSIONAL (3D) ISING MODEL[J]. ACTA METALLURGICA SINICA,2016,52(10):1311-1325. |
| APA | Zhang Zhidong.(2016).MATHEMATICAL STRUCTURE AND THE CONJECTURED EXACT SOLUTION OF THREEDIMENSIONAL (3D) ISING MODEL.ACTA METALLURGICA SINICA,52(10),1311-1325. |
| MLA | Zhang Zhidong."MATHEMATICAL STRUCTURE AND THE CONJECTURED EXACT SOLUTION OF THREEDIMENSIONAL (3D) ISING MODEL".ACTA METALLURGICA SINICA 52.10(2016):1311-1325. |
入库方式： OAI收割
来源：金属研究所
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