Theta-point behavior of diluted polymer solutions: Can one observe the universal logarithmic corrections predicted by field theory?

Abstract

In recent large scale Monte-Carlo simulations of various models of Theta-point polymers in three dimensions Grassberger and Hegger found logarithmic corrections to mean field theory with amplitudes much larger than the universal amplitudes of the leading logarithmic corrections calculated by Duplantier in the framework of tricritical O(n) field theory. To resolve this issue we calculate the universal subleading correction of field theory, which turns out to be of the same order of magnitude as the leading correction for all chain lengths available in present days simulations. Borel resummation of the renormalization group flow equations also shows the presence of such large corrections. This suggests that the published simulations did not reach the asymptotic regime. To further support this view, we present results of Monte-Carlo simulations on a Domb-Joyce like model of weakly interacting random walks. Again the results cannot be explained by keeping only the leading corrections, but are in fair accord with our full theoretical result. The corrections found for the Domb-Joyce model are much smaller than those for other models, which clearly shows that the effective corrections are not yet in the asymptotic regime. All together our findings show that the existing simulations of Theta-polymers are compatible with tricritical field theory since the crossover to the asymptotic regime is very slow. Similar results were found earlier for self avoiding walks at their upper critical dimension d=4.