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; Statistical-mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences
	N. H. March; Z. D. Zhang
	2010 ; 2010
发表期刊	Journal of Mathematical Chemistry ; Journal of Mathematical Chemistry
ISSN	0259-9791 ; 0259-9791
卷号	47 期号:1 页码:520-538
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.; 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.
部门归属	[zhang, z. d.] chinese acad sci, shenyang natl lab mat sci, inst met res, 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, shenyang natl lab mat sci, inst met res, 72 wenhua rd, shenyang 110016, peoples r china;zdzhang@imr.ac.cn ; [zhang, z. d.] chinese acad sci, shenyang natl lab mat sci, inst met res, 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, shenyang natl lab mat sci, inst met res, 72 wenhua rd, shenyang 110016, peoples r china;zdzhang@imr.ac.cn
关键词	Statistical-mechanical Models Statistical-mechanical Models Many-body Interactions Many-body Interactions Partition Partition Functions Functions Thermodynamic Consequences Thermodynamic Consequences Orthorhombic Ising Lattices Orthorhombic Ising Lattices One-component Plasma One-component Plasma Recent Conjectured Recent Conjectured Solution Solution Bare Coulomb Field Bare Coulomb Field Slater Sum Slater Sum Pair Potentials Pair Potentials Renormalization Group Renormalization Group Critical Exponents Critical Exponents Magnetic Equation Magnetic Equation Critical-point Critical-point
URL	查看原文 ; 查看原文
WOS记录号	WOS:000273162000040 ; WOS:000273162000040
引用统计	被引频次：6[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/321006/31374
专题	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, Statistical-mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences[J]. Journal of Mathematical Chemistry, Journal of Mathematical Chemistry,2010, 2010,47, 47(1):520-538, 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.