Diagrammatic Approaches to the Excluded Volume Problem

Comparison with Diagrammatic Approaches to the Excluded Volume Problem 

In many-body theory, it is fashionable to generate new approximations by summing infinite classes of the diagrams of perturbation theory (whether or not the approximations give anything useful). The recent diagrammatic approaches to the excluded volume problem can be related to the following crude approximation to the simple Edwards field (6.24). Let 

Apart frem differences in notation. Figs. 5 and 6a are seen to be identical to the approximation developed by Curro, Blatz, and Pings,when the 

The physical defect of the approximation (6,47) and (6.48), apart from its neglect of the specification of the chain end(s), lies in the fact that the approximate excluded volume field is made up of a sum of contributions from only a portion of the total chain (of contour length L). This arises because the G s in (6.48), which are defined through the inhomogeneous diffusion equations, vanish when s — s or s — s 0. Thus the actual limits of integration must be j s s.  

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