Theta-point behavior of diluted polymer solutions: Can one observe the universal logarithmic corrections predicted by field theory?
PRE 60, 2071 (1999) 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 c...
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| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
31-08-1999
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | PRE 60, 2071 (1999) 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. |
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| DOI: | 10.48550/arxiv.cond-mat/9908474 |