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 \( {{\mathbb R}^d} \) that contain at most one particle in each cube of a given partition of the space \( {{\mathbb R}^d} \) 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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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 3, pp. 369–384, March, 2011.
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Petrenko, S.M., Rebenko, O.L. & Tertychnyi, M. Quasicontinuous approximation in classical statistical mechanics. Ukr Math J 63, 425–442 (2011). https://doi.org/10.1007/s11253-011-0513-0
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DOI: https://doi.org/10.1007/s11253-011-0513-0