Linear polymers in dimension

Probably our most important work is a high-precision study of the critical exponents u and 2A4 — 7 (and in particular the hyperscaling law dv = 2A4 — 7) and universal amplitude ratios for SAWs in both two and 

Another startling conclusion from this study concerns the interpenetration ratio 4 (cf. eq. (2.14)), and goes to the heart of polymer theory. But this requires a brief historical digression. 

For several decades, most work on the behavior of long-chain polymer molecules in dilute solution has been based on the so-called two-parameter theory in one or another of its variants traditional (Flory-type),f pseudo-traditional (modified Flory-type) or modem (continuous-chain-type). All two-parameter theories predict that in the limit of zero concentration, the mean-square end-to-end distance RI), the mean-square 

Ht may be related to the apparent fact that the confluent exponent A2/A1 is very close to an integer (namely, it is 2). 

But our Monte Carlo data show precisely the opposite behavior J is a decreasing and convex function of N, which approaches a limiting value w 0.247 as AT — oo (Fig. 2.15). The same behavior was found by Nickel. Indeed, there is experimental evidence that for real polymers in a sufficiently good solvent, the approach to is also from above, contrary to the two-parameter theoryThis behavior was considered to be a perplexing anomalous effect , and various explanations were advanced. What is going on here  

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