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MATHEMATICAL STRUCTURE AND THE CONJECTURED EXACT SOLUTION OF THREEDIMENSIONAL (3D) ISING MODEL
Zhang Zhidong
Corresponding AuthorZhang Zhidong(zdzhang@imr.ac.cn)
2016-10-01
Source PublicationACTA METALLURGICA SINICA
ISSN0412-1961
Volume52Issue:10Pages:1311-1325
AbstractIn 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.
KeywordIsing model mathematical structure exact solution topological property algebraic property geometric property
Funding OrganizationNational Natural Science Foundation of China
DOI10.11900/0412.1961.2016.00336
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[51331006] ; National Natural Science Foundation of China[51590883]
WOS Research AreaMetallurgy & Metallurgical Engineering
WOS SubjectMetallurgy & Metallurgical Engineering
WOS IDWOS:000390080900015
PublisherSCIENCE PRESS
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.imr.ac.cn/handle/321006/123352
Collection中国科学院金属研究所
Corresponding AuthorZhang Zhidong
AffiliationChinese Acad Sci, Inst Met Res, Shenyang Natl Lab Mat Sci, Shenyang 110016, Peoples R China
Recommended Citation
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.
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