Calculation and minimization of the free energy, critical exponent

2 Calculation and minimization of the free energy critical exponent 

We shall now calculate the free energy associated with the trial probability. 

Let us first evaluate the mean energy of the system [see (8.1.68) and (8.1.70)]. The chain energy is immediately obtained 

When N is large, the contributions corresponding to large values of n play a crucial role. But, for such values of n, the law P (r) is very flat defining the excluded volume parameter zt by the dimensionless expression  

Let us minimize the free energy by writing the condition 8F/d (k) = 0. Since according to (8.1.82) 

---