E J Janse van Rensburg and A R Rechnitzer 2004 J. Phys. A: Math. Gen. 37 6875 doi:10.1088/0305-4470/37/27/002
Multiple Markov chain Monte Carlo study of adsorbing self-avoiding walks in two and in three dimensions
E J Janse van Rensburg1 and A R Rechnitzer2
Show affiliationsA self-avoiding walk adsorbing on a line in the square lattice, and on a plane in the cubic lattice, is studied numerically as a model of an adsorbing polymer in dilute solution. The walk is simulated by a multiple Markov chain Monte Carlo implementation of the pivot algorithm for self-avoiding walks. Vertices in the walk that are visits in the adsorbing line or plane are weighted by eβ. The critical value of β, where the walk adsorbs on the adsorbing line or adsorbing plane, is determined by considering energy ratios and approximations to the free energy. We determine that the critical values of β are 
In addition, the value of the crossover exponent is determined: 
Metric quantities, including the mean square radius of gyration, are also considered, as well as rescaling of the specific heat and free energy, as the critical point is approached.
- PACS
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61.25.H- Macromolecular and polymers solutions; polymer melts
61.20.Ja Computer simulation of liquid structure
05.40.Fb Random walks and Levy flights
- MSC
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82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
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Issue 27 (9 July 2004)
Received 27 January 2004
Published 22 June 2004
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Multiple Markov chain Monte Carlo study of adsorbing self-avoiding walks in two and in three dimensions
E J Janse van Rensburg and A R Rechnitzer 2004 J. Phys. A: Math. Gen. 37 6875
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