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Diagrams irreducible diagram

Fig. 2. Some of the diagrams occurring in Mt. Articulation points are indicated by arrows, (a) and (b) are irreducible diagrams (c) and (d) are linked reducible and unlinked respectively. Fig. 2. Some of the diagrams occurring in Mt. Articulation points are indicated by arrows, (a) and (b) are irreducible diagrams (c) and (d) are linked reducible and unlinked respectively.
The variables that appear in the single parts are therefore statistically independent. By virtue of Eq. (50) it follows that all cross products of linked reducible or unlinked parts must vanish in Mn. In consequence only the irreducible diagrams contribute to M . Furthermore, if we consider the contribution of the irreducible diagram in Figs. 2a to M3 we have the terms... [Pg.22]

Consider then an irreducible diagram with melon bonds in the wth semi-invariant, consisting of n lines and k nodes whose composition is k. The k nodes can be selected from the N2 defects in... [Pg.23]

Eq. (55) is the sum of all simple irreducible diagrams that can be formed among the k nodes, every bond representing an ffj function. (Thus every node is multiply connected. If k = 2 then B is exceptional and corresponds to the graph of two nodes and an /l2> bond.) It should be noted that flf is zero when i and j coincide (cf. Eq. (44)). [Pg.24]

Fig. 3. Examples of irreducible diagrams making zero contribution. Fig. 3. Examples of irreducible diagrams making zero contribution.
The loop expansion of a vertex irreducible quantify containing external vertices is represented by all vertex irreducible diagrams containing only screened interactions. Diagrams, in which a chain-like structure not contain-... [Pg.71]

Now we observe that we can set any I-irreducible diagram at each vertex of X. Thus a vertex function vm f is associated with each vertex of a tree the following expression defines v / ... [Pg.399]

In particular, the simple-tree approximation described in Section 6.2 can be recovered by retaining from among the irreducible diagrams only those which contain one polymer line and no more. This is equivalent to the approximation in which one keeps only the term Z,( 1 x S) and this result is obtained by setting... [Pg.403]

This transformation shows that the reducible diagrams contributing to Green s functions have a tree structure and that the vertices of these trees are P-irreducible diagrams which define the vertex functions (see Appendix I). [Pg.454]

As r(M) is the generating function associated with the P-irreducible diagrams, we see that to zero-loop order, we have... [Pg.461]

Fig. 12.6. (a) 2-P-irreducible diagram, (b) 2-P-reducible diagram, containing a cascade of insertions (like Russian dolls ). [Pg.485]

The diagrams contributing to (S, S) are either I-reducible (by cutting an interaction line see Fig. 12.12) or I-irreducible. The contributions of I-reducible diagrams can be factorized and are therefore easy to calculate. The simplest I-irreducible diagrams are shown in Fig. 12.13. [Pg.515]

By summing the contributions of the I-reducible and I-irreducible diagrams, to first-orders in z and we find... [Pg.515]

Fig. 12.13. 1-irreducible diagrams of order two and three corresponding to 2"(S, S) and their contributions to first-orders in e. [Pg.516]

A general expression of the structure function in terms of the contributions of I-irreducible diagrams... [Pg.632]

Thus, it is natural to introduce the generating functions of the I-irreducible diagrams, namely... [Pg.633]

The summation of the trees made of irreducible parts can be made in a very simple way and we can proceed as in Section 2.3 when we described the simple-tree approximation. For more details, the reader may refer to Chapter 10, Section 2.5.5. We see that an I-irreducible diagram of order N can be dressed with side branches, in all possible ways, and that this dressing amounts to replacing the factor / by a factor... [Pg.633]

Vertex function which m legs, for polymer diagrams these vertex functions are represented by connected I-irreducible diagrams... [Pg.922]

A pair of reducible points in an irreducible graph is a pair of points that are connected by a bond and/or that are a pair of articulation points. When a pair of reducible points is removed from a diagram, the diagram becomes disconnected into two or more parts. Some parts may simply be bonds with no point on each end, if the pair of reducible points were connected by one or more bonds. Some parts may be collections of field points connected by bonds and containing some bonds with no point on one end, if the pair of reducible points were a pair of articulation points. Some parts may be collections of field points and root points, containing some bonds with no point at one end, if the original... [Pg.5]

The terms of the series can be rearranged and represented through irreducible diagrams of the following form ... [Pg.100]

Each irreducible diagrajn is defined by a graph where each point (molecule) is connected with, at least, two other points by an / bond. An exceptional case of two interacting molecuha is introduced to make the pattern complete as the smallest irreducible diagram. To clarify the last term, wc present two diagrams... [Pg.100]

The number of topologically difTerent diagram.s for every n-partirle subset increases with n sharply. Eg. there exist 3 four-particle, 10 five-particle, and 56 six-particle irreducible diagrams. [Pg.100]


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See also in sourсe #XX -- [ Pg.583 ]




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