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We introduce a new method for the enumeration of self-avoiding walks based on the lace expansion. We also introduce an algorithmic improvement, called the two-step method, for self-avoiding walk enumeration problems. We obtain significant extensions of existing series on the cubic and hypercubic lattices in all dimensions d ≥ 3: we enumerate 32-step… (More)

- Nathan Clisby
- Physical review letters
- 2010

We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we use to obtain large samples of walks on the cubic lattice of up to 33x10{6} steps. Consequently the critical exponent nu for three-dimensional self-avoiding walks is determined to great accuracy; the final estimate is nu=0.587 597(7). The method can be adapted to… (More)

- Nathan Clisby, Barry M. McCoy, C. N. Yang
- 2008

We evaluate the virial coefficients Bk for k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. Further analysis provides evidence that negative virial… (More)

- Nathan Clisby, Iwan Jensen
- 2012

We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm.… (More)

- Damien A Fordham, Kevin T Shoemaker, Nathan H Schumaker, H Reşit Akçakaya, Nathan Clisby, Barry W Brook
- Biology letters
- 2014

Forecasts of range dynamics now incorporate many of the mechanisms and interactions that drive species distributions. However, connectivity continues to be simulated using overly simple distance-based dispersal models with little consideration of how the individual behaviour of dispersing organisms interacts with landscape structure (functional… (More)

- Marvin Bishop, Nathan Clisby, Paula A Whitlock
- The Journal of chemical physics
- 2008

The equation of state of hard hyperspheres in nine dimensions is calculated both from the values of the first ten virial coefficients and from a Monte Carlo simulation of the pair correlation function at contact. The results are in excellent agreement. In addition, we find that the virial series appears to be dominated by an unphysical singularity or… (More)

We give an introduction to the lace expansion for self-avoiding walks, with emphasis on self-avoiding polygons, and with a focus on combinatorial rather than analytical aspects. We derive the lace expansion for self-avoiding walks, and show that this is equivalent to taking the reciprocal of the self-avoiding walk generating function. We list some of the… (More)

- Nathan Clisby, Barry M. McCoy, C. N. Yang
- 2008

We present new results for the virial coefficients Bk with k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8.

- Nathan Clisby, Burkhard Dünweg
- Physical review. E
- 2016

The universal asymptotic amplitude ratio between the gyration radius and the hydrodynamic radius of self-avoiding walks is estimated by high-resolution Monte Carlo simulations. By studying chains of length of up to N=2^{25}≈34×10^{6} monomers, we find that the ratio takes the value R_{G}/R_{H}=1.5803940(45), which is several orders of magnitude more… (More)

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