Quasicontinuous approximation in classical statistical mechanics |
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Authors: | S. M. Petrenko O. L. Rebenko M.V. Tertychnyi |
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Affiliation: | 1.Kyiv,Ukraine;2.Kyiv,Ukraine |
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Abstract: | Within the framework of classical statistical mechanics, we consider infinite continuous systems of point particles with strong superstable interaction. A family of approximate correlation functions is defined to take into account solely the configurations of particles in the space mathbb Rd {{mathbb R}^d} that contain at most one particle in each cube of a given partition of the space mathbb Rd {{mathbb R}^d} into disjoint hypercubes of volume a d : It is shown that the approximations of correlation functions thus defined are pointwise convergent to the exact correlation functions of the system if the parameter of approximation a approaches zero for any positive values of the inverse temperature β and fugacity z: This result is obtained both for two-body interaction potentials and for many-body interaction potentials. |
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