Equilibrium ensembles and Landau-Ginzburg model

1 Osmotic pressure and generating function of the Green s functions 

The one-field model gives a description of the approximate grand canonical ensembles introduced in Chapter 11, Section 5. These ensembles, called equilibrium ensembles , depend on only two fugacities, which determine respectively the average number of polymers and the average number of monomers (constituting the polymers). In the continuous case, a connected partition function J(/, a) can be associated with this ensemble it is defined by 

RELATIONS BETWEEN CHAIN THEORY AND FIELD THEORY 

Here/and e are the two fugacities determining the ensemble. This equation is analogous to (11.5.1) (since S oc N and e- oc ). When J(/, a) is known, the osmotic pressure II can be expressed, in parametric form, as a function of the average number C of polymers per unit volume and of the average total area per unit volume (( can be considered as proportional to the monomer concentration). 

The function 3(/ a) has a simple interpretation in field theory. In fact, by Fourier transformation, (11.5.1) becomes 

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