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

TL;DR

This paper investigates the logarithmic corrections in Theta-point polymer solutions, revealing that current simulations do not reach the asymptotic regime and are consistent with tricritical field theory due to slow crossover effects.

Contribution

The study calculates the universal subleading correction to field theory and demonstrates its significance in interpreting Monte-Carlo simulation results for Theta polymers.

Findings

Large corrections are present at current chain lengths.

Simulations are not in the asymptotic regime due to slow crossover.

Corrections vary among different models, affecting their agreement with 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.