The method of auxiliary fields

1 The method of auxiliary fields. Our first aim is to decouple the chains by linearizing the interaction term. We introduce an auxiliary field y (r) obeying 

The integral (A 5.12 is defined as the properly normalized integration over the Fourier components 

To complete the definition we note that - (r) is real, implying 

In the functional integral (A 5.12) we may shift y (r) as in normal Gaussian integrals. Substituting 

Grand Canonical Description of Solutions at Finite Concentration 

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