On statistical mechanics of systems with highly singular two-body potentials

A finite volume statistical mechanics for highly singular two-body potentials is studied. The case of “point” hard-core particles (Lennard-Jones type two-body potentials) is discussed and the mathematical background for this physical idealization is given. Firstly the definition of a self-adjoint Ha...

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Bibliographic Details
Published in:Annals of physics 1976-11, Vol.102 (1), p.108-128
Main Author: Zagrebnov, V.A
Format: Article
Language:English
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Summary:A finite volume statistical mechanics for highly singular two-body potentials is studied. The case of “point” hard-core particles (Lennard-Jones type two-body potentials) is discussed and the mathematical background for this physical idealization is given. Firstly the definition of a self-adjoint Hamiltonian for such a system is considered. Then a natural cutoff procedure for two-body highly singular potentials is proposed. The main result is the proof of a convergence theorem for partition sums (or free energies) when the cutoff parameter is removed to infinity. The question of stability of the cutoff interactions is also discussed. These results are illustrated by a consideration of the Lennard-Jones potential (12-6). Our results are valid in all dimensions greater than two and for potentials being not inevitably spherically symmetric.
ISSN:0003-4916
1096-035X
DOI:10.1016/0003-4916(76)90257-8