Self-avoiding walks and polygons on the triangular lattice

Journal of Statistical Mechanics: Theory and Experiment

Volumn , Issue 10, 2004, Pages

  Jensen, Iwan ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

critical exponents and amplitudes (theory); series expansions

Indexed keywords

EID: 84901038154     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2004/10/P10008     Document Type: Article

References (31)

1. Caracciolo S, Guttmann A J, Jensen I, Pelissetto A, Rogers A N and Sokal A D 2004 Correction-to-scaling exponents for two-dimensional self-avoiding walks Preprint cond-mat/0409355
2. Caracciolo S, Pelissetto A and Sokal A D 1990 Universal distance ratios for two-dimensional self-avoiding walks: corrected conformal invariance predictions J. Phys. A: Math. Gen. 23 L969
3. Cardy J L 1994 Mean area of self-avoiding loops Phys. Rev. Lett. 72 1580
4. Cardy J L and Guttmann A J 1993 Universal amplitude combinations for self-avoiding walks, polygons and trails J. Phys. A: Math. Gen. 26 2485
5. Cardy J L and Mussardo G 1993 Universal properties of self-avoiding walks from two-dimensional field theory Nucl. Phys. B 410 451
6. Cardy J L and Saleur H 1989 Universal distance ratios for two-dimensional polymers J. Phys. A: Math. Gen. 22 L601
7. 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
8. Conway A R and Guttmann A J 1996 Square lattice self-avoiding walks and corrections to scaling Phys. Rev. Lett. 77 5284
9. Delest M P and Viennot G 1984 Algebraic languages and polyominoes enumeration Theor. Comput. Sci. 34 169
10. Enting I G 1980 Generating functions for enumerating self-avoiding rings on the square lattice J. Phys. A: Math. Gen. 13 3713
11. Enting I G and Guttmann A J 1992 Self-avoiding rings on the triangular lattice J. Phys. A: Math. Gen. 25 2791
12. Guttmann A J 1989 Asymptotic analysis of power-series expansions Phase Transitions and Critical Phenomena vol 13 ed C Domb and J L Lebowitz (New York: Academic) pp 1-234
13. Guttmann A J and Conway A R 2001 Square lattice self-avoiding walks and polygons Ann. Comb. 5 319
14. Guttmann A J and Yang Y S 1990 Universal distance ratios for 2d saws: series results J. Phys. A: Math. Gen. 23 L117
15. Hughes B D 1995 Random Walks and Random Environments vol I Random Walks (Oxford: Clarendon)
16. Janse van Renburg E J 2000 The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles (Oxford: Oxford University Press)
17. Jensen I 2000 Size and area of square lattice polygons J. Phys. A: Math. Gen. 33 3533
18. Jensen I 2003 Counting polyominoes: a parallel implementation for cluster computing ICCS 2003: Computational Science (Lecture Notes in Computer Science vol 2659) ed P M A Sloot, D Abramson, A V Bogdanov, J J Dongarra, A Y Zomaya and Y E Gorbachev (Berlin: Springer) pp 203-12
19. Jensen I 2003 A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice J. Phys. A: Math. Gen. 36 5731
20. Jensen I 2004 Enumeration of self-avoiding walks on the square lattice J. Phys. A: Math. Gen. 37 5503
21. Jensen I and Guttmann A J 1999 Self-avoiding polygons on the square lattice J. Phys. A: Math. Gen. 32 4867
22. Lin K Y 2000 Universal amplitude combinations for self-avoiding walks and polygons on the honeycomb lattice Physica A 275 197
23. Lin K Y and Huang J X 1995 Universal amplitude ratios for self-avoiding walks on the Kagomé lattice J. Phys. A: Math. Gen. 28 3641
24. Lin K Y and Lue S J 1999 Universal amplitude combinations for self-avoiding polygons on the Kagomé lattice Physica A 270 453
25. Madras N and Slade G 1993 The Self-Avoiding Walk (Boston, MA: Birkhäuser)
26. Nienhuis B 1982 Exact critical point and critical exponents of O (n) models in two dimensions Phys. Rev. Lett. 49 1062
27. Nienhuis B 1984 Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas J. Stat. Phys. 34 731
28. Owczarek A L, Prellberg T, Bennett-Wood D and Guttmann A J 1994 Universal distance ratios for interacting two-dimensional polymers J. Phys. A: Math. Gen. 27 L919
29. Privman V and Redner S 1985 Tests of hyperuniversality for self-avoiding walks J. Phys. A: Math. Gen. 18 L781
30. Richard C, Guttmann A J and Jensen I 2001 Scaling function and universal amplitude combinations for self-avoiding polygons J. Phys. A: Math. Gen. 34 L495
31. Richard C, Jensen I and Guttmann A J 2003 Scaling function for self-avoiding polygons TH2002: Proc. Int. Congr. on Theoretical Physics (Paris), Supplement ed D Iagolnitzer, V Rivasseau and J Zinn-Justin (Basel: Birkhäuser) pp 267-77 [cond-mat/0302513]