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A General Cluster Expansion and the Definition of Self‐Consistent n ‐Site Approximations in the Theory of Disordered Systems
Author(s) -
Fischbeck H. J.
Publication year - 1974
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220620211
Subject(s) - cluster expansion , series (stratigraphy) , cluster (spacecraft) , mathematics , approximations of π , operator (biology) , series expansion , type (biology) , statistical physics , zero (linguistics) , distribution (mathematics) , mathematical physics , mathematical analysis , pure mathematics , physics , quantum mechanics , chemistry , computer science , paleontology , biochemistry , linguistics , philosophy , repressor , transcription factor , gene , programming language , ecology , biology
A general cluster expansion of the averaged transition operator of a disordered system in terms of the distribution functions of its constituents is given. Self‐consistent n ‐site approximations are defined by requiring that a truncated version of this series should be zero in an effective medium. In the alloy case these are shown to be equivalent to previously derived approximations. For amorphous systems a new type of n ‐site approximations is obtained.