Continuous spin model de Gennes

In the absence of interaction between spins belonging to the same site (b = 0), the weight1W reduces to the weight 00 W 

It can immediately be verified that, when there is no nearest-neighbour coupling and no interaction, 

Let us now consider the Green s function corresponding to the case without interaction 

Expanding °W in powers of 1. W and applying Wick s theorem in the averages (see Appendix A), we can represent °G(r1,r2 A) by diagrams. The diagrams correspond to random walks on the lattice. It can be verified that this function depends only on the result is the same as in the case where there is only one field 

We also note that the line joining rt and ry contains an arbitrary number of links and that a weight exp( — AJ) is associated with each link. Formula (11.3.6) is a direct consequence of these observations, and, for a given lattice, it establishes an exact correspondence between an interacting-chain theory and a zero-component field theory. 

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