Three-dimensional terminally attached self-avoiding walks and bridges

@article{Clisby2015ThreedimensionalTA,
  title={Three-dimensional terminally attached self-avoiding walks and bridges},
  author={Nathan Clisby and Andrew R. Conway and Anthony J. Guttmann},
  journal={arXiv: Statistical Mechanics},
  year={2015}
}
We study terminally attached self-avoiding walks and bridges on the simple cubic lattice, both by series analysis and Monte Carlo methods. We provide strong numerical evidence supporting a scaling relation between self-avoiding walks, bridges, and terminally attached self-avoiding walks, and posit that a corresponding amplitude ratio is a universal quantity. 
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References

SHOWING 1-10 OF 32 REFERENCES
Compressed self-avoiding walks, bridges and polygons
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk
On the scaling limit of planar self-avoiding walk
A planar self-avoiding walk (SAW) is a nearest neighbor random walk path in the square lattice with no self-intersection. A planar self-avoiding polygon (SAP) is a loop with no self-intersection. In
Conformal invariance of the 3D self-avoiding walk.
TLDR
It is shown that if the three-dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half-space and in a sphere, and by Monte Carlo simulations these predictions are found to be excellent agreement.
Calculation of the connective constant for self-avoiding walks via the pivot algorithm
TLDR
The connective constant for self-avoiding walks on the simple cubic lattice is estimated to be μ = 4.684 039 931 ± 0.000 000 027, to unprecedented accuracy, using a novel application of the pivot algorithm.
Accurate estimate of the critical exponent nu for self-avoiding walks via a fast implementation of the pivot algorithm.
TLDR
A fast implementation of the pivot algorithm for self-avoiding walks is introduced, which is used to obtain large samples of walks on the cubic lattice of up to 33x10{6} steps, and the critical exponent nu is determined to great accuracy.
Self-avoiding walk enumeration via the lace expansion
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
Two-dimensional polymer networks at a mixed boundary: Surface and wedge exponents
Abstract:We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface
Simulations of grafted polymers in a good solvent
We present improved simulations of three-dimensional self-avoiding walks with one end attached to an impenetrable surface on the simple cubic lattice. This surface can either be a-thermal, having
Efficient Implementation of the Pivot Algorithm for Self-avoiding Walks
TLDR
The pivot algorithm for self-avoiding walks has been implemented in a manner which is dramatically faster than previous implementations, enabling extremely long walks to be efficiently simulated, and promises to be widely useful.
...
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