Title




Statisticalmechanical models with separable manybody interactions: especially partition functions and thermodynamic consequences
 
Author




 
Abstract




We start from a classical statisticalmechanical theory for the internal energy in terms of three and fourbody 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 twobody interactions is the socalled onecomponent 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 quantummechanical assemblies are treated, again with separable manybody interactions. The example chosen is that of an Nbody inhomogeneous extended system generated by a onebody potential energy V(r). The focus here is on the diagonal element of the canonical density matrix: the socalled Slater sum S(r, β), related to the pf by $${{\rm pf}(\beta) = \int {S({\bf r}, \beta)}d\vec {r}}$$, β = (k B T)−1. The Slater sum S(r, β) can be related exactly, via a partial differential equation, to the onebody 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 twobody forces. Finally, to avoid perturbation series, the work concludes with some proposals to allow the treatment of extended assemblies in which regions of longrange ordered magnetism exist in the phase diagram. One of us (Z.D.Z.) has recently proposed a putative pf for a threedimensional (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. 
 
Language




English
 
Source (journal)




Journal of mathematical chemistry.  Basel
 
Publication




Basel
:
2010
 
ISSN




02599791
 
Volume/pages




47
:1
(2010)
, p. 520538
 
ISI




000273162000040
 
Full text (Publisher's DOI)




 
