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Linked-cluster expansions for the correlation functions of lattice systems

Published online by Cambridge University Press:  24 October 2008

John W. Essam
John W. Essam
Affiliation:
Department of Mathematics, Westfield College, University of London
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Extract

A method of deriving power series expansions for the correlation functions of lattice systems is described. The concept of lattice constants for rooted graphs is introduced and it is shown how the correlation functions can be expanded in terms of the lattice constants for connected graphs only. The weight functions in the expansions depend on correlation functions for finite systems and may, therefore, be determined by computer methods. This work is an extension of a method previously developed for the free energy. Applications to spin systems, percolation problems and the lattice gas are considered and sum rules for the weight functions are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 2 , March 1970 , pp. 523 - 534
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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