Summarizing Overview

Abstract

In this part we have discussed an internally consistent evaluation of the theory to one-loop order. It verifies the asymptotic power laws predicted by scaling theory by showing that the assumed limiting behavior of the scaling functions indeed holds to the order considered. More importantly, it provides us with quantitative predictions for the scaling functions in all the crossover regime. As a general rule the crossover functions vary extremely smoothly and show no pronounced structure. This is by no means surprising for a scale invariant system. It, however, implies that asymptotic power laws are attained only slowly. It also implies that parameter values like c, where the dilute behavior shall cross over to semidilute behavior, are not well defined. Also the temperature blob model is not meaningful as a model of scaling functions. Data analysis based on such oversimplified pictures is likely to result in effective parameter range dependent exponents. Quite generally it must be noted that power law fits, which have become so popular with the advent of scaling theory, often miss relevant information contained in more precise data and sometimes even have led to a misinterpretation of the results.