Improved lower bounds on the connective constants for two-dimensional self-avoiding walks

Journal of Physics A: Mathematical and General

Volumn 37, Issue 48, 2004, Pages 11521-11529

  Jensen, Iwan ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10844222287     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/48/001     Document Type: Article

References (21)

1. Ahlherg R and Janson S 1981 Upper hounds for the connective constant Technical Report Department of Mathematics, Uppsala University
2. Alm S E 1993 Upper hounds for the connective constant of self-avoiding walks Comb. Probab. Comput. 2 115-36
3. Alm S E 2004 in preparation. Courtesy of a private communication from R Parviainen and contained in his PhD Thesis, Connective Properties of Archimedean and Laves Lattices, Uppsala dissertations in mathematics 34 Uppsala University
4. Alm S E and Parviainen R 2004 Bounds for the connective constant of the hexagonal lattice J. Phys. A: Math. Gen. 37 549-60
5. Conway A R. Enting I G and Guttmann A J 1993 Algebraic techniques for enumerating self-avoiding walks on the square lattice J. Phys. A: Math. Gen. 26 1519-34
6. Conway A R and Guttmann A J 1993 Lower bound on the connective constant for square lattice self-avoiding walks J. Phys. A: Math. Gen. 26 3719-24
7. Guttmann A J 1983 Bounds on connective constants for self-avoiding walks J. Phys. A: Math. Gen. 16 2233-8
8. Guttmann A J 1983 Bounds on self-avoiding walks on directed square lattices J. Phys. A: Math. Gen. 16 3885-984
9. 2 ) lattice Preprint cond-mat/0410241
10. Hammersley J M and Morton K W 1954 Poor man's Monte Carlo J. R. Stat. Soc. B 16 23-38
11. Jensen I 2003 A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice J. Phys. A: Math. Gen. 36 5731-45
12. Jensen I 2004 Enumeration of self-avoiding walks on the square lattice J. Phys. A. Math. Gen. 37 5503-24 (Preprint cond-mat/0404728)
13. Jensen I 2004 Self-avoiding walks and polygons on the triangular lattice J. Stat. Mech.: Th. Exp. submitted (Preprint cond-mat/0409039)
14. Jensen I 2004 Self-avoiding walks and polygons on the honeycomb lattice in preparation
15. Jensen I and Guttmann A J 1998 Self-avoiding walks, neighbour-avoiding walks and trails on semiregular lattices. J. Phys. A : Math. Gen. 30 8137-45
16. Kesten H 1963 On the number of self-avoiding walks. J. Math. Phys. 4 960-9
17. Knuth D E 1969 Seminumerical Algorithms. The Art of Computer Programming vol 2 (Reading. MA: Addison-Wesley)
18. Madras N and Slade G 1993 The Self-Avoiding Walk (Boston. MA: Birkhäuser)
19. Nienhuis B 1982 Exact critical point and critical exponents of O(n) models in two dimensions Phys. Rev. Lett. 49 1062-5
20. Nienhuis B 1984 Critical behavior of two- dimensional spin models and charge asymmetry in the coulomb gas J. Stat. Phys. 34 731-61
21. d Electron. J. Comb. 7 R21