Journal of Statistical Physics

, Volume 78, Issue 3–4, pp 877–892 | Cite as

Transformation and topological reduction of cluster expansions usingm-bonds

  • Hung-Chang Chiu
  • David A. Kofke


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.

Key Words

Cluster series diagrammatic methods topological reduction graph theory 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Hung-Chang Chiu
    • 1
  • David A. Kofke
    • 1
  1. 1.Department of Chemical EngineeringState University of New York at BuffaloBuffalo

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