Model, perturbation calculation and diagrams

The only difference between the model used here and the standard continuous model comes from the fact that the two-body term is attractive and that we add a repulsive three-body term. The weight associated with a configuration of a set of l chains reads. 

Of course, we assume, as in Chapter 10, that there exists a short range cut-off s0 on the chain, so as to ensure that perturbation calculations give finite results. It is expected that the properties of long chains do not really depend on s0. Nevertheless, the situation is not as simple as in the purely repulsive case treated in Chapter 10. As we shall see later, the introduction of three-body terms leads to serious difficulties which fortunately can be overcome. 

In the following, we consider only monodisperse systems and we study tricritical systems by using the direct renormalization method. It is also possible to proceed indirectly by introducing a tricritical field theory and the correspondence which exists between field theory and polymer theory. This approach 

we use the direct renormalization method which relies on a slightly different conceptual approach. Nevertheless the points of view are equivalent and the results obtained through field theory can be directly recovered, (as we shall now show) by using more recent results obtained (1985) by Duplantier.15 

In the monodisperse case, there are two basic dimensionless parameters which define the strength of the interactions 

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