Transfer matrices for the partition function of the Potts model on lattice strips with toroidal and Klein-bottle boundary conditions

Physica A: Statistical Mechanics and its Applications

Volumn 364, Issue , 2006, Pages 231-262

  Chang, Shu Chiuan ^a   Shrock, Robert ^b  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b STONY BROOK UNIVERSITY   (United States)

Author keywords

Partition function; Potts model; Transfer matrices

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; HONEYCOMB STRUCTURES; LATTICE CONSTANTS; POLYNOMIALS;

HONEYCOMB LATTICES; PARTITION FUNCTION; POTTS MODEL; TRANSFER MATRICES;

TRANSFER FUNCTIONS;

EID: 33645161405     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2005.08.076     Document Type: Article

References (59)

1. R.B. Potts Proc. Camb. Phil. Soc. 48 1952 106
2. F.Y. Wu Rev. Mod. Phys. 54 1982 235
3. P. Kasteleyn, and C. Fortuin J. Phys. Soc. Jpn. (Suppl.) 26 1969 11
4. C. Fortuin, and P. Kasteleyn Physica 57 1972 536
5. R. Shrock Physica A 283 2000 388
6. R. Shrock, in: The Proceedings of the 1999 British Combinatorial Conference, BCC99, July, 1999
7. (Physica A 281, 221 (2000)).
8. S.-C. Chang, and R. Shrock Physica A 286 2000 189
9. S.-C. Chang, and R. Shrock Physica A 296 2001 183
10. S.-C. Chang, and R. Shrock Physica A 296 2001 234
11. S.-C. Chang, and R. Shrock Int. J. Mod. Phys. B 15 2001 443
12. S.-C. Chang, and R. Shrock Phys. Rev. E 64 2001 066116
13. S.-C. Chang, R. Shrock, in: The Proceedings of the CRM Workshop on Tutte Polynomials, 2001
14. (Adv. Appl. Math. 32 (2004) 44).
15. S.-C. Chang, J. Salas, and R. Shrock J. Stat. Phys. 107 2002 1207
16. S.-C. Chang, J. Jacobsen, J. Salas, and R. Shrock J. Stat. Phys. 114 2004 763
17. S.-C. Chang, and R. Shrock Physica A 346 2005 400
18. S.-C. Chang, and R. Shrock Physica A 347 2005 314
19. N.L. Biggs, R.M. Damerell, and D.A. Sands J. Combin. Theory B 12 1972 123
20. H. Saleur Commun. Math. Phys. 132 1990 657
21. H. Saleur Nucl. Phys. B 360 1991 219
22. J. Salas, and A. Sokal J. Stat. Phys. 104 2001 609
23. S.-C. Chang, and R. Shrock Physica A 296 2001 131
24. S.-C. Chang, and R. Shrock Physica A 301 2001 301
25. N.L. Biggs, Algebraic Graph Theory, 1st ed. 1974, 2nd ed. 1993, Cambridge University Press, Cambridge.
26. R.C. Read, W.T. Tutte, Chromatic Polynomials, in: Selected Topics in Graph Theory, vol. 3, Academic Press, New York, 1988, p. 15.
27. N.L. Biggs, and G.H. Meredith J. Combin. Theory B 20 1976 5
28. R.J. Baxter J. Phys. A 19 1986 2821
29. R.J. Baxter J. Phys. A 20 1987 5241
30. N.L. Biggs J. Combin. Theory B 82 2001 19
31. N.L. Biggs Bull. London Math. Soc. 34 2002 129
32. N.L. Biggs, London School of Economics Centre for Discrete and Applicable Mathematics, Report LSE-CDAM-2000-04.
33. H.W.J. Blöte, and M.P. Nightingale Physica A 112 1982 405
34. J. Jacobsen, and J. Salas J. Stat. Phys. 104 2001 701
35. J. Jacobsen, J. Salas, and A.D. Sokal J. Stat. Phys. 112 2003 921
36. W.T. Tutte, Chromials, in: Lecture Notes in Mathematics, vol. 411, 1974, 243;
37. Graph Theory, Encyclopedia of Mathematics and Applications, vol. 21, Addison-Wesley, Menlo Park, 1984.
38. N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, http://www.research.att.com/ ∼ njas/sequences/.
39. P. Flajolet, and M. Noy Discrete. Math. 204 1999 203
40. N.L. Biggs, and R. Shrock J. Phys. A (Letts.) 32 1999 L489
41. S.-C. Chang, and R. Shrock Physica A 292 2001 307
42. R.P. Stanley Enumerative Combinatorics vol. 2 1999 Cambridge University Press Cambridge
43. F.R. Bernhart Disc. Math. 204 1999 73
44. S.-C. Chang, and R. Shrock Physica A 316 2002 335
45. B. Bollobás Modern Graph Theory 1998 Springer New York
46. S.-C. Chang, and R. Shrock Ann. Phys. 290 2001 124 cond-mat/0004129
47. R. Shrock, and S.-H. Tsai J. Phys. A Lett. 32 1999 L195 L200
48. R. Shrock, and S.-H. Tsai Physica A 275 2000 429
49. R. Shrock, and S.-H. Tsai Phys. Rev. E 55 1997 5165
50. D. Welsh Complexity: Knots, Colourings and Counting 1993 Cambridge University Press Cambridge
51. J. Jacobsen, J. Salas, cond-mat/0407444.
52. R. Shrock Phys. Lett. A 261 1999 57
53. S.-C. Chang, and R. Shrock Physica A 290 2001 402
54. S.-C. Chang, and R. Shrock Physica A 301 2001 196
55. N.L. Biggs Linear Algebra Appl. 356 2002 3
56. H. Kluepfel, R. Shrock, YITP-99-32;
57. H. Kluepfel, Stony Brook Thesis (July, 1999).
58. S.-Y. Kim, and R. Creswick Phys. Rev. E 63 2001 066107
59. S.-C. Chang, and R. Shrock J. Stat. Phys. 112 2003 815