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Transformation and topological reduction of cluster expansions usingm-bonds

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Abstract

We introduce the notion of an “m-bond” and show how it may be used to manipulate the cluster expansions that describe the equilibrium properties of classical fluids. Anm-bond has a constant value of −1, and its presence affects the sign and symmetry number of a graph. We further define an “m-product,” which is formed by summing all graphs obtained by addingm-bonds to join field points in the (usual) product graph. It is shown that the logarithm of a sum of graphs can be written in terms of theirm-products. The formalism is used to demonstrate a few well-known results concerning cluster expansions. Also, a generalization of them-product is introduced, and with it a theorem is presented that relates graphs composed off-fonds to those that contain bothf- and (f+1)-bonds. Such “frustrated” graphs are useful in understanding approximations such as the Percus-Yevick formula, and also in performing numerical calculations.

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Authors and Affiliations

  1. Department of Chemical Engineering, State University of New York at Buffalo, 14260-4200, Buffalo, New York

    Hung-Chang Chiu & David A. Kofke

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  1. Hung-Chang Chiu
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  2. David A. Kofke
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Chiu, HC., Kofke, D.A. Transformation and topological reduction of cluster expansions usingm-bonds. J Stat Phys 78, 877–892 (1995). https://doi.org/10.1007/BF02183692

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