Temperature-time duality exemplified by Ising magnets and quantum-chemical many electron theory

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	Temperature-time duality exemplified by Ising magnets and quantum-chemical many electron theory
	Z. D. Zhang; N. H. March
	2011
发表期刊	Journal of Mathematical Chemistry
ISSN	0259-9791
卷号	49 期号:7 页码:1283-1290
摘要	In this work, we first present a detailed analysis of temperature-time duality in the 3D Ising model, by inspecting the resemblance between the density operator in quantum statistical mechanics and the evolution operator in quantum field theory, with the mapping beta = (k (B) T)(-1) -> it. We point out that in systems like the 3D Ising model, for the nontrivial topological contributions, the time necessary for the time averaging must be infinite, being comparable with or even much larger than the time of measurement of the physical quantity of interest. The time averaging is equivalent to the temperature averaging. The phase transitions in the parametric plane (beta, it) are discussed, and a singularity (a second-order phase transition) is found to occur at the critical time t (c) , corresponding to the critical point beta (c) (i.e, T (c) ). It is necessary to use the 4-fold integral form for the partition function for the 3D Ising model. The time is needed to construct the (3 + 1)D framework for the quaternionic sequence of Jordan algebras, in order to employ the Jordan-von Neumann-Wigner procedure. We then turn to discuss quite briefly temperature-time duality in quantum-chemical many-electron theory. We find that one can use the known one-dimensional differential equation for the Slater sum S(x, beta) to write a corresponding form for the diagonal element of the Feynman propagator, again with the mapping beta -> it.
部门归属	[zhang, z. d.] chinese acad sci, inst met res, shenyang natl lab mat sci, shenyang 110016, peoples r china. [zhang, z. d.] chinese acad sci, int ctr mat phys, shenyang 110016, peoples r china. [march, n. h.] univ antwerp, dept phys, b-2020 antwerp, belgium. [march, n. h.] univ oxford, oxford, england.;zhang, zd (reprint author), chinese acad sci, inst met res, shenyang natl lab mat sci, 72 wenhua rd, shenyang 110016, peoples r china;zdzhang@imr.ac.cn
关键词	Temperature-time Duality 3d Isingmodel The Temperature Averaging Quantum-chemical Many-electron Theory Lattices Conjectures
URL	查看原文
WOS记录号	WOS:000292816000007
引用统计	被引频次：9[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/321006/30935
专题	中国科学院金属研究所
推荐引用方式 GB/T 7714	Z. D. Zhang,N. H. March. Temperature-time duality exemplified by Ising magnets and quantum-chemical many electron theory[J]. Journal of Mathematical Chemistry,2011,49(7):1283-1290.
APA	Z. D. Zhang,&N. H. March.(2011).Temperature-time duality exemplified by Ising magnets and quantum-chemical many electron theory.Journal of Mathematical Chemistry,49(7),1283-1290.
MLA	Z. D. Zhang,et al."Temperature-time duality exemplified by Ising magnets and quantum-chemical many electron theory".Journal of Mathematical Chemistry 49.7(2011):1283-1290.