Upper Bounds for the Connective Constant of Self-Avoiding Walks

@article{Alm1993UpperBF,
  title={Upper Bounds for the Connective Constant of Self-Avoiding Walks},
  author={Sven Erick Alm},
  journal={Combinatorics, Probability & Computing},
  year={1993},
  volume={2},
  pages={115-136}
}
We present a method for obtaining upper bounds for the connective constant of selfavoiding walks. The method works for a large class of lattices, including all that have been studied in connection with self-avoiding walks. The bound is obtained as the largest eigenvalue of a certain matrix. Numerical application of the method has given improved bounds for all lattices studied, e.g. ji < 2.696 for the square lattice, n < 4.278 for the triangular lattice and n < 4.756 for the simple cubic lattice… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 20 references

Upper bounds for the connectivity constant

R. Ahlberg, S. Janson
Preprint, Dept. of Math. Uppsala University • 1981
View 8 Excerpts
Highly Influenced

Bounds on self-avoiding walks on directed square lattices

A. J. Guttmann
J. Phys. A • 1983
View 3 Excerpts
Highly Influenced

Percolation processes II. The connective constant

J. M. Hammersley
Proc. Camb. Phil. Soc • 1957
View 3 Excerpts
Highly Influenced

The extension of self-avoiding random walk series in two dimensions

A. J. Guttmann, J. Wang
J. Phys. A • 1991
View 2 Excerpts

On the critical behaviour of self-avoiding walks

A. J. Guttmann
J. Phys. A • 1987
View 1 Excerpt

Bounds on connective constants for self-avoiding walks

A. J. Guttmann
J. Phys. A • 1983
View 1 Excerpt

Exact critical point and critical exponent of O(n) models in two dimensions

B. Nienhuis
Phys. Rev. Lett • 1982
View 1 Excerpt

The critical behaviour of two-dimensional self-avoiding random walks

P. Grassberger
Z. Phys. B - Condensed Matter • 1982
View 1 Excerpt

On the zero-field susceptibility in the d = 4, n = 0 limit: analysing for confluent logarithmic singularities

A. J. Guttmann
J. Phys. AW L103-106 • 1978
View 1 Excerpt

Self-avoiding walks on oriented square lattices

A. Malakis
J. Phys. A • 1975
View 1 Excerpt

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