A discussion concerning the nature of universal functions in polymer theory

2 A discussion concerning the nature of universal functions in polymer theory 

As was shown in Chapter 10, a mathematical correspondence exists between polymer models and models that are used to study critical magnetic systems (and others), as, for instance, the Ising and the Heisenberg models. Thus, one might think that for all these critical phenomena, the universal functions in the scaling laws appear in a very similar way. However, the analogy is not complete, and in what follows it will be shown that, in reality, the universal functions appear in a more pleasant form in polymer theory than in magnetic theories. 

In fact, it is always possible to compare the properties of polymers in moderately dilute or semi-dilute solutions with those which the same polymers would have in a very dilute solution. In other words, the size of an isolated JV-link polymer in a solvent can always be used as a scale length to describe the 

This fact also explains why the concept of broken symmetry which seems crucial in the theory of magnetism (and also in field theory) does not appear at all in polymer theory. 

Of course, these differences have no intrinsic character. The theoretical framework is fundamentally the same but the physical context is different. The difference comes only from the fact that in the two models, the physical quantities correspond to peculiar mathematical entities and that, in polymer 

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