Monte Carlo renormalization of hard sphere polymer chains in two to five dimensions View Full Text


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Article Info

DATE

1981-12

AUTHORS

K. Kremer, A. Baumgärtner, K. Binder

ABSTRACT

A renormalization group for polymer chains with hard-core interaction is considered, where a chain ofN0 links of lengthl0 and hard-core diameterh0 is mapped onto a chain ofN1=N0/s links of lengthl1 and hard-core diameterh1. The lengthl1 is defined in terms of suitable interior distances of the original chain, andh1 is found from the condition that the end-to-end distance is left invariant. This renormalization group procedure is carried through by various Monte-Carlo methods (simple sampling is found advantageous for short enough chains or high dimensionalities, while dynamic methods involving “kinkjumps” or “reptation” are used else). Particular attention is paid to investigate systematic errors of the method by checking the dependence of the results on bothN0 ands. It is found that for dimensionalitiesd=2, 3 only the nontrivial fixed-point is stable, where upon iteration the ratio δk=hk/lk tends to nonzero fixed-point value δ*, while ford=4,5 the method converges to the gaussian fixed point with δ*=0. Taking both statistical and systematic errors into account, we estimate the exponentv asv=0.74±0.01 (d=2) andv =0.59±0.01 (d=3). The results are consistent with the expected crossover exponents ϕ =1/2 (d=3) and ϕ=1 (d=2), respectively. More... »

PAGES

331-341

References to SciGraph publications

  • 1977-12. Application of the Monte Carlo method for evaluating the Niemeijer-van Leeuwen cumulant expansion in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • 1977-07. Theoretical methods of polymer statistics in LA RIVISTA DEL NUOVO CIMENTO (1971-1977)
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/bf01292850

    DOI

    http://dx.doi.org/10.1007/bf01292850

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    40 schema:description A renormalization group for polymer chains with hard-core interaction is considered, where a chain ofN0 links of lengthl0 and hard-core diameterh0 is mapped onto a chain ofN1=N0/s links of lengthl1 and hard-core diameterh1. The lengthl1 is defined in terms of suitable interior distances of the original chain, andh1 is found from the condition that the end-to-end distance is left invariant. This renormalization group procedure is carried through by various Monte-Carlo methods (simple sampling is found advantageous for short enough chains or high dimensionalities, while dynamic methods involving “kinkjumps” or “reptation” are used else). Particular attention is paid to investigate systematic errors of the method by checking the dependence of the results on bothN0 ands. It is found that for dimensionalitiesd=2, 3 only the nontrivial fixed-point is stable, where upon iteration the ratio δk=hk/lk tends to nonzero fixed-point value δ*, while ford=4,5 the method converges to the gaussian fixed point with δ*=0. Taking both statistical and systematic errors into account, we estimate the exponentv asv=0.74±0.01 (d=2) andv =0.59±0.01 (d=3). The results are consistent with the expected crossover exponents ϕ =1/2 (d=3) and ϕ=1 (d=2), respectively.
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