Statistical-mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences

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	Statistical-mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences
	N. H. March ; Z. D. Zhang
刊名	Journal of Mathematical Chemistry
	2010
卷号	47 期号:1 页码:520-538
关键词	Statistical-mechanical models Many-body interactions Partition functions Thermodynamic consequences orthorhombic ising lattices one-component plasma recent conjectured solution bare coulomb field slater sum pair potentials renormalization group critical exponents magnetic equation critical-point
ISSN号	0259-9791
中文摘要	We start from a classical statistical-mechanical theory for the internal energy in terms of three-and four-body correlation functions g(3) and g(4) for homogeneous atomic liquids like argon, with assumed central pair interactions phi(r(ij)). The importance of constructing the partition function (pf) as spatial integrals over g(3), g(4) and phi is stressed, together with some basic thermodynamic consequences of such a pf. A second classical example taken for two-body interactions is the so-called one-component plasma in two dimensions, for a particular coupling strength treated by Alastuey and Jancovici (J Phys (France) 42:1, 1981) and by Fantoni and Tellez (J Stat Phys 133: 449, 2008). Again thermodynamic consequences provide a particular focus. Then quantum-mechanical assemblies are treated, again with separable many-body interactions. The example chosen is that of an N-body inhomogeneous extended system generated by a one-body potential energy V(r). The focus here is on the diagonal element of the canonical density matrix: the so-called Slater sum S(r, beta), related to the pf by pf(beta) = integral S(r, beta) d (r) over right arrow, beta = (k(B)T)(-1). The Slater sum S(r, beta) can be related exactly, via a partial differential equation, to the one-body potential V(r), for specific choices of V which are cited. The work of Green (J Chem Phys 18: 1123, 1950), is referred to for a generalization, but now perturbative, to two-body forces. Finally, to avoid perturbation series, the work concludes with some proposals to allow the treatment of extended assemblies in which regions of long-range ordered magnetism exist in the phase diagram. One of us (Z. D. Z.) has recently proposed a putative pf for a three-dimensional (3D) Ising model, based on two, as yet unproved, conjectures and has pointed out some important thermodynamic consequences of this pf. It would obviously be of considerable interest if such a pf, together with conjectures, could be rigorously proved.
原文出处	://WOS:000273162000040
公开日期	2012-04-13
内容类型	期刊论文
源URL	[http://210.72.142.130/handle/321006/31374]
专题	金属研究所_中国科学院金属研究所
推荐引用方式 GB/T 7714	N. H. March,Z. D. Zhang. Statistical-mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences[J]. Journal of Mathematical Chemistry,2010,47(1):520-538.
APA	N. H. March,&Z. D. Zhang.(2010).Statistical-mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences.Journal of Mathematical Chemistry,47(1),520-538.
MLA	N. H. March,et al."Statistical-mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences".Journal of Mathematical Chemistry 47.1(2010):520-538.