A J Barrett and A Pound 1980 J. Phys. A: Math. Gen. 13 1811 doi:10.1088/0305-4470/13/5/040
Self-avoiding lattice walks with high coordination and small excluded volume
A J Barrett and A Pound
Show affiliationsA self-avoiding walk on a lattice may be characterised by the 'excluded volume ratio' V=closest approach of two centres/stop length. Walks to other than nearest-neighbour sites on a simple cubic lattice have high coordination numbers and low values of the excluded volume ratio. Some general results are presented for a class of these walks. Exact enumerations and Monte Carlo simulations have been made of the total number CN and the mean square length (RN2) for two examples of this class. These measurements are used to test the 'universality hypothesis' which contends that CN approximately N1/6 mu N and (RN2) approximately N6/5 as N to infinity , irrespective of the value of V. The data are in reasonable agreement with these statements, and the universality hypothesis is found to provide a good basis for the description of a self-avoiding walk.
- PACS
- MSC
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82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
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Issue 5 (1 May 1980)
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Self-avoiding lattice walks with high coordination and small excluded volume
A J Barrett and A Pound 1980 J. Phys. A: Math. Gen. 13 1811
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