Entropy and continuous limit

Consider a random system. With each state SI, of this system, we can associate a probability pt. In statistical mechanics, the entropy of the system is defined by 

If the system is a chain of origin O, on a lattice and if ZN is the number of allowed configurations for the chain, we can write 

for a chain with excluded volume and large values of N, we obtain from (2.3.4) 

In this formula, the quantities p and ZD depend on the lattice but y is a universal exponent. 

In a more general way, we may consider, on the lattice, chains whose points repel one another with short-range interactions. This condition will appear in the fact that with each configuration 11 is associated a probability p(Sl) 

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