Fields and sets of chains analytical method

Moreover, we observe that the mean value of the product of 2p components oyi0( is always proportional to (n/V ) 1 + p. Thus, in the limit n - 0, all such mean values vanish except the quantities 

the property that we used above is now proved both for Sarma s and Hilhorst s models. 

The correspondence existing between polymer theory and zero-component field theory can also be established analytically as was shown by Emery6 and also by Kosmas and Freed.7 A more general approach has been found by Duplantier.8 We shall follow it here but with a broader point of view. We shall choose a continuous model, ignoring all possible divergences. More precisely, in what follows we define partition functions 3TG(r. r2j S. SM) analogous to the 2 g (r,. . ., r2W N,.. ., NH) introduced at the beginning of Section 3. With them, we associate the Laplace transforms 

Moreover, it is clear that such a relation also implies that the connected Green s functions are the Laplace transforms of connected partition functions (without index G). We call it the Laplace-de Gennes transformation. 

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