Ten thousand off‐lattice self‐avoiding walks of 500 steps were generated using a new algorithm combining the features of the enrichment procedure of Wall and Erpenbeck and the dimerization procedure of Alexandrowicz. The mean square endpoint separation was tabulated as a function of the number of steps in the walk and fitted to the equation , where N is the number of steps in the walk. A value for γ of was obtained, in excellent agreement with values for on‐lattice walks. Earlier investigators using off‐lattice self‐avoiding walks probably obtained higher values of γ because they were limited to 100‐step walks.
REFERENCES
1.
See M. Barber and B. Ninham, Random and Restricted Walks (Gordon and Breach, New York 1971) for a survey of applications.
2.
and
P.
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4.
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this quantity was discussed earlier by W. W. Wood, in Physics of Simple Liquids, edited by H. N. V. Temperley, J. S. Rowlinson, and G. S. Rushbroke (North‐Holland, Amsterdam, 1968) p. 115.
12.
To keep the program from flagging adjacent pearls as overlapping because of roundoff errors, the step size was in practice set to 1.001.
13.
The program used an additive pseudorandom number generator as described in
B.
Green
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Klem
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6
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The 90% confidence limits for a parameter are computed by taking the root‐mean‐square deviation of the 10 data points, dividing by to get an estimate of the standard deviation of the average, then multiplying by the 90% confidence limit for Student’s t distribution with 9 degrees of freedom, See for example, P. Hoel, Introduction to Mathematical Statistics (Wiley, New York, 1954).
15.
A direct comparison with any of the workers cited earlier is not possible because each used a different model from the one used here. Bruns’ model also had unconstrained rotational and bond angles, but employed a uniform distribution in bond angle, quite different from the uniform distribution in spherical angle of our model.
16.
P. Gans (private communication).
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© 1973 The American Institute of Physics.
1973
The American Institute of Physics
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