MATHEMATICAL STRUCTURE AND THE CONJECTURED EXACT SOLUTION OF THREEDIMENSIONAL (3D) ISING MODEL

doi:10.11900/0412.1961.2016.00336

IMR OpenIR

	MATHEMATICAL STRUCTURE AND THE CONJECTURED EXACT SOLUTION OF THREEDIMENSIONAL (3D) ISING MODEL
	Zhang Zhidong
通讯作者	Zhang Zhidong(zdzhang@imr.ac.cn)
	2016-10-01
发表期刊	ACTA METALLURGICA SINICA
ISSN	0412-1961
卷号	52 期号:10 页码:1311-1325
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.
关键词	Ising model mathematical structure exact solution topological property algebraic property geometric property
资助者	National Natural Science Foundation of China
DOI	10.11900/0412.1961.2016.00336
收录类别	SCI
语种	英语
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
WOS类目	Metallurgy & Metallurgical Engineering
WOS记录号	WOS:000390080900015
出版者	SCIENCE PRESS
引用统计	被引频次：2[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.imr.ac.cn/handle/321006/123352
专题	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.