Applicability of the Standard Renormalized Field Theory to the Strong Coupling Regime for the Domb–Joyce Model

Abstract

We present a field theoretic analysis of high-precision Monte Carlo data for the Domb–Joyce model. This analysis shows the ability of the standard formalism to describe the data. In the Domb–Joyce model of a polymer chain the repulsion between two segments at the same point is varied between zero (random walk) up to infinity (self avoiding walk). To increase the excluded volume we even include a repulsion between segments at neighbor points. The data for the end-to-end distance, the radius of gyration and the partition function clearly shows the existence of two branches of universal behavior, corresponding to weak or strong excluded volume. The nonuniversal parameters of the renormalized theory have to be considered as fitting parameters to one given quantity (We have chosen the end-to-end distance). Given these nonuniversal parameters, we can predict the variation of all other measured quantities. Good agreement with the MC data is found for all data, including the strong coupling branch. We conclude, in contrast to some claims in the literature, that the standard formalism of the renormalized field theory can be used even for renormalized couplings greater than the fixed point value (strong coupling branch).