Conformational problem of a molecular chain

Wilson (1972) has calculaled the values of the critical indices 7 and i] for a system with the Hamiltonian 

In that paper the correlation functions (the Green functions, the ordered G reen functions, etc.) near the critical point were expressed as series in o and e, where e = d — /. In particular, the Green function G k) for = 0 was calculated, that corresponds to the permeability x,. (see Equation 2.6 38), which, in its turn, is proportional to the scattered light intensity (sec Equation 2.3-133) for which 

The correlation functions w ere calculated by Wilson using the diagrammatic technique and the renormalization procedure. 

A problem of random self avoiding walks on a lattice with interactions (with due ciccouiit for the excluded volume) has been considered by de Gennes (1972) in his pioneering work. 

If rAf(h) denotes the number of random self-avoiding walk trajectories (with interaction) of iV steps (units), connecting the points 0 and li, then the Green function in momentum space takes the form 

---