Field theory of critical phenomena: quantitative analysis beyond powerlaws

We present a brief introduction to the theory of renormalization, where we base our discussion on the dilatation group and concentrate on the structural aspects. We then in particular consider the crossover between the Gaussian and the nontrivial fixed point. Crossover functions show two branches, depending on the physical coupling strength. We present recent Monte Carlo data for self-repelling random walks (polymer solutions) that verify this two branched structure. We finally discuss aspects important for a perturbative calculation of the crossover functions. Using data for a variety of observables in polymer solutions we demonstrate that the theory has reached the stage of quantitative success. (C) 1998 Elsevier Science B.V. All rights reserved.